First of all, I suggest using the install script as is, without  modifying it. (then you would not have this problem, you can always install a different version of PostgreSQL later)

A default pg_hba.conf looks like this, you should not need to change this:

local   all             postgres                                peer
local   all             all                                     peer
host    all             all             127.0.0.1/32            md5
host    all             all             ::1/128                 md5

A example of odoo database settings:

; Database settings
db_user = odoo
db_password = odoo_user_password
db_port = 5432
db_host = localhost
db_maxconn = 64
dbfilter = .*

check your postgre service is it running or not

I cannot comment your messages because "30 karma is required to perform this action"… Therefore I edit this message for answer to Hengky Zhang and Ivan. Sorry.

Hi Hengky Zhang.
postgres is running. htop displays:

PID USER      PRI  NI  VIRT   RES   SHR S CPU% MEM%   TIME+  Command
 1156 postgres   20   0  199M 11052 10940 S  0.0  0.4  0:00.04 ├─ /opt/PostgreSQL/9.3/bin/postgres -D /opt/PostgreSQL/9.3/data
 1195 postgres   20   0 60260   400   272 S  0.0  0.0  0:00.06 │  ├─ postgres: stats collector process
 1194 postgres   20   0  200M   880   656 S  0.0  0.0  0:00.09 │  ├─ postgres: autovacuum launcher process
 1193 postgres   20   0  199M   304   248 S  0.0  0.0  0:00.10 │  ├─ postgres: wal writer process
 1192 postgres   20   0  199M  1116  1044 S  0.0  0.0  0:00.10 │  ├─ postgres: writer process
 1191 postgres   20   0  199M   260   192 S  0.0  0.0  0:00.00 │  ├─ postgres: checkpointer process
 1175 postgres   20   0 58168   172   156 S  0.0  0.0  0:00.00 │  └─ postgres: logger process

-------------------------------------------

Hi Ivan. /opt/PostgreSQL/9.3/data/pg_hba.conf contains:

# TYPE  DATABASE        USER            ADDRESS                 METHOD

# "local" is for Unix domain socket connections only
local   all             all                                     md5
# IPv4 local connections:
host    all             all             127.0.0.1/32            md5
# IPv6 local connections:
host    all             all             ::1/128                 md5
# Allow replication connections from localhost, by a user with the
# replication privilege.
#local   replication     postgres                                md5
#host    replication     postgres        127.0.0.1/32            md5
#host    replication     postgres        ::1/128                 md5

I can change the /etc/odoo-server.conf file like this:

[...]

db_password = PasswordGivenToPostgresqlDuringInstallation

[…]

I'm going to read this page carefully: http://www.postgresql.org/docs/9.3/static/auth-pg-hba-conf.html

The solution is near…

-------------------------

I read carefully the auth-pg-hba-conf.html webpage, set pg_hba.conf and restarted postgresql then odoo, but I still have the same server error described in my first message.

As regards pg_hba.conf, I tried this:

local   all             all                             peer

then this:

host    all              all             127.0.0.1/32           ident

… but it failed every time. :(

When I add a password to odoo user like this:

ALTER ROLE odoo WITH PASSWORD odoo_user_password_for_postgresql

… and then I modify /etc/odoo-server.conf consequently:

db_password = odoo_user_password_for_postgresql

… before trying different configurations for pg_hba.conf, it fails again.

-----------------------------

Kristof Hardy:
I changed:
    db_host = False
    db_password = False
… by:
    db_host = localhost
    db_password = odoo_user_password
… in /etc/odoo-server.conf, then I added a odoo password to postgresql from psql like this:
    ALTER ROLE odoo WITH PASSWORD 'odoo_user_password';
At last I set /opt/PostgreSQL/9.3/data/pg_hba.conf as you recommended:
    local   all             postgres                                peer
    local   all             all                                     peer
    host    all             all             127.0.0.1/32            md5
    host    all             all             ::1/128                 md5

It works! :) At last! Great!

Thank everybody to have helped me, especially Kristof Hardy and Ivan.