The next generation wireless communications systems demand higher data rates transmission in order to meet the high quality services. Orthogonal Frequency Division Multiplexing (OFDM) offers high data rate, high Spectral Efficiency (SE), and immunity against narrow band interference. Spectral efficiency is one of the major issues in wireless communication system. The spectral efficiency of a channel is a measure of the number of bits per second per Hz. The spectral efficiency is presented in many ways in the literature. In wireless communication system SE depends on Bit Error Rate (BER), coding rate and modulation technique. This study investigates the SE and Bit Error Rate (BER) performance OFDM system over AWGN channel with different QAM modulation techniques. Simulation results show that minimum SE obtained with the 16QAM modulation technique with coding rate ½ at lower Signal to Noise Ratio (SNR). The comparative show that minimum BER can be achieved with the 16QAM modulation technique.