In this paper, We analyzes how a synchronization error affects receiving system when using OFDM(Orthogonal Frequency Division Multiplexing) transmission method in wireless LAN channel environment in which we can efficiently transmit wide-band information data. As a performance improvement method, performance distortion can be improved by applying convolution coding. As a result, in OFDM system, we could see that the higher a frequency offset is, the worse performance will be, and we could see that there was performance improvement by applying convolution coding in OFDM system in order to reach (BER=$10^{-3}$). However, when we use 64QAM (64Quadrature Amplitude Modulation), there was a huge influence between carriers by frequency offset at 0.05, 0.1.