Relay transmission is promising for future wireless systems due to its significant cooperative diversity gain. The performance of dual-hop semi-blind amplify-and-forward (AF) relaying systems was extensively investigated, for transmissions over Rayleigh fading channels or Nakagami-m fading channels with integer fading parameter. For the general Nakagami-m fading with arbitrary m values, the exact closed-form system performance analysis is more challenging. In this paper, we explicitly derive the moment generation function (MGF), probability density function (PDF) and moments of the end-to-end signal-to-noise ratio (SNR) over arbitrary Nakagami-m fading channels with semi-blind AF relay. With these results, the system performance evaluation in terms of outage probability, average symbol error probability, ergodic capacity and diversity order, is conducted. The analysis developed in this paper applies to any semi-blind AF relaying systems with fixed relay gain, and two major strategies for computing the relay gain are compared in terms of system performance. All analytical results are corroborated by simulation results and they are shown to be efficient tools to evaluate system performance.