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You can change Docker's storage base directory (where container and images go) using the -g option when starting the Docker daemon.

• Ubuntu/Debian: edit your /etc/default/docker file with the -g option: DOCKER_OPTS="-dns 8.8.8.8 -dns 8.8.4.4 -g /mnt"

1. Stop docker: service docker stop. Verify no docker process is running ps faux
2. Double check docker really isn't running. Take a look at the current docker directory: ls /var/lib/docker/
3. Move the /var/lib/docker directory to your new partition: mv /var/lib/docker /mnt/pd0/docker
4. Make a symlink: ln -s /mnt/pd0/docker /var/lib/docker
5. Take a peek at the directory structure to make sure it looks like it did before the mv: ls /var/lib/docker/ (note the trailing slash to resolve the symlink)
6. Start docker back up service docker start
7. restart your containers

Important ! See also this link with another method