Cooperative communication using multiple relays improves quality of service (QoS) parameters of a communication system. To verify this improvement, accurate analysis must be done considering the various fading channels and probability density function (PDF) or cumulative distribution function (CDF) of signal-to-noise ratio (SNR) in relays and destination. In this paper, using the moment-generating function (MGF) method and considering Nakagami-m fading channel, the outage probability and effective capacity are analyzed. Obtaining the closed-form expression of outage probability and effective capacity in Nakagami-m fading channel includes complex mathematical calculations; thus, the Rayleigh fading channel is assumed to be a special case of Nakagami-m distribution to achieve simpler mathematical equations. Simulation results verify the mathematical analysis in terms of effective capacity and outage probability.