For convenience of studying the performance of the maximal ratio combining (MRC) diversity system under condition of non-identically distributed (i.n.d.) Nakagami-m fading channels, both the exact solution of the system outage probability and a method for obtaining the numerical solution of the outage probability are concluded based on the probability density function of the output signal to noise ratio (SNR). In accordance with the moment generation function (MGF) of the output SNR, the expressions of Chernoff upper bound of the average symbol error rate (ASER), the asymptotic diversity gain and the effective diversity gain under different modulation methods are obtained, and the correctness is verified by simulation. The simulation results indicate that with the increase of the number of diversity branches, the systems average symbol error rate decreases, and the diversity gain is enhanced. Simultaneously, the degree of fading unbalance for each branch has a greater impact on the system performance. Besides, the smaller the degree of channel fading, the greater its impact on the outage probability.