The following procedure applies to version 1.5 and later of Docker.

To enable users other than root and users with sudo access to be able to run Docker commands:

Add the user into docker Group

For current user
$ sudo usermod -aG docker $(whoami)
For any other user account:
$ sudo usermod -aG docker <username>

Now logout the user account and login back (or) exit from the terminal and login back

Note:
  1. Users who can run Docker commands have effective root control of the system. Only grant this privilege to trusted users.