In this paper, we propose an antenna selection algorithm for down link MIMO SDMA OFDM system. For each user, the data rate corresponding to each transmit antenna is maximized using the optimal bit loading algorithm. A data rate matrix is constructed and used for the antenna selection algorithm assuming the base station (BS) knows the signalto-noise ratio on all antenna-user pairs of all sub-carriers. In addition to exploiting the multi-user diversity gain, all users are served fairly by the BS. The fairness is achieved through weighting the data rate matrix by a weighting matrix with coefficients inversely proportional to the number of times served for each user. Jain's fairness index is used as a measure of the fairness. Simulation results show that a significant increase in the data rate is a achieved compared to the ultimately fair round Robin algorithm, while satisfying a reasonable fairness.