We study the performance of adaptive M-ary quadrature amplitude modulation (MQAM) in wireless cellular system with Nakagami fading and log-normal shadowing. An interference-limited system is assumed and the statistic of co-channel interference is analyzed. Our analysis shows that the instantaneous signal-to-interference ratio (SIR) in cellular system with Nakagami fading and log-normal shadowing can be approximated as having the log-normal distribution. We derive the probability density function (PDF) of the instantaneous SIR and use it to evaluate the spectrum efficiency of MQAM in cellular systems. The impacts of Nakagami fading, shadowing and the target bit error rate (BER) on average throughput and average outage probability are presented and discussed.