This paper studies the fairness optimization of dynamic multiuser multicarrier allocation in the cellular downlink of MIMO orthogonal frequency division multiple access (OFDMA) systems. The varying capacity demands of different users motivate the fairness problem. In the resource allocation approaches that maximizing the sum rate or minimizing the total power often leads to poor fairness among users. The allocation is prone to starvation situation for the users with deep fading subchannels. Hence, this work considers the fairness issue and proposes to maximize the minimum rate surplus, where the rate surplus is defined as the difference between the demand data rate and the resulting allocated data rate. The fairness is inverse proportional to the gap of the maximum rate surplus to the minimum rate surplus among all users. In this work, the design of the precoding and decoding matrices for the MIMO structure is also developed. To solve the optimization problem, an iterative algorithm is proposed to optimize the subcarrier assignment with low complexity. Simulation results on multiuser MIMO environment show that the proposed algorithm strikes the balance between sum rate and fairness. Comparing with the stateof-the-art works, the proposed algorithm shows an advantage in keeping the sum rate while the fairness is significantly improved.