We derive a closed-form expression for the outage probability (OP), which is an important performance metric used to measure the probability that the target error rate performance of wireless systems exceeds a specified value, of multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems with best antenna selection under independent, but not necessarily identical distributed Nakagami-m fading. To gain further insights on the performance, the asymptotic approximation for OP, which reveals the diversity gain, is presented. We show that the diversity gain is solely determined by the fading severity parameters and increases with number of antennas at all nodes.