Accessing Redis server on AWS

I am not able to connect to my Redis server from remote AWS instance (both instances are in same VPC though)...

I have launched CentOS 6 instance and launched Redis server. I can confirm that server is running:

tcp        0      0 *:6379     *:*    LISTEN   891/redis-server *
tcp        0      0 *:6379     *:*    LISTEN   891/redis-server *

I have set AWS security group to be:

Custom TCP | port 6379 | 0.0.0.0/0

I am able to connect to the Redis server from the same instance using redis-cli but when I try to do it from some other AWS instance I get:

Could not connect to Redis at ec2-*.compute.amazonaws.com:6379: No route to host