In this paper, we investigate the performance for diversity reception schemes over composite fading channels using a mixture gamma (MG) distribution. With high accuracy, the MG distribution can approximate a variety of composite fading channel models and provide mathematically tractable properties. In contrast to previous analysis approaches which require complicated signal-to-noise ratio statistics, we derive simple closed-form expressions of a diversity and array gain for important diversity reception schemes such as maximum ratio combining and selection combining by adopting the MG distribution. Our results lead to meaningful insights for determining the system performance with parameters of the MG distribution. We observe that for various transmitted signal modulations, our proposed analysis can be expressed with the general number of receiver branches over independent and non-identically distributed composite fading cases. Simulation results confirm that the derived diversity and array gain match well with the empirical results.