The combination of Multiple-Input Multiple-Output (MIMO) with Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for achieving high performance with very high data rates in 4G broadband wireless communications. Nevertheless, one major disadvantage of MIMO-OFDM systems lies in a prohibitively large Peak-to-Average Power Ratio (PAPR) of the transmitted signal on each antenna. Indeed, the performance of the receivers is very sensitive to nonlinear distortions caused by the High Power Amplifier (HPA). Furthermore, Crosstalk can take place before or after the power amplifiers designated herein as nonlinear and linear crosstalk, respectively. In this paper, we extend the efficient Neural Network Predistorter (NNPD) proposed in [1] to MIMO-OFDM systems and equally demonstrate that nonlinear crosstalk significantly affects the performance of NNPD. Along, we propose a new Crossover Neural Network Predistorter (CO-NNPD) model to compensate simultaneously for crosstalk and HPA nonlinearity in MIMO-OFDM systems. The Levenberg-Marquardt algorithm (LM) is used for neural network training, which has proven [3] to exhibit a very good performance with lower computation complexity and faster convergence than other algorithms used in literature. This paper is supported with simulation results for the Alamouti STBC MIMO OFDM system in terms of Bit Error Rate (BER) in Rayleigh fading channel.