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Neural networks can easily fall into a local extremum and have slow convergence rate. Quantum Genetic Algorithm (QGA) has features of small population size and fast convergence. Based on the investigation of QGA, we propose a novel neural network model, Radial Basis Function (RBF) networks optimized by Quantum Genetic Algorithm (QGA-RBF model). Then we investigate the performance of the proposed QGA-RBF on solving MIMO-OFDM signal detection problem. A novel signal detector based on QGA-RBF for MIMO-OFDM system is also proposed. The simulation results show that the proposed detector has more powerful properties in bit error rate than QGA based detector, RBF based detector and MMSE algorithm based detector, namely a 4-6 dB gain in performance can be achieved. The performance of the proposed detector is closer to optimal, compared with the other detectors.