Cooperative spectrum sensing is proposed to overcome some problem such as multipath fading and shadowing and to improve spectrum sensing performance. There are different combining methods for cooperative spectrum sensing: hard decision method and soft decision method. In this paper, we analysis the performance of cooperative spectrum sensing with distance based weight that is kind of a soft decision rule for cognitive radio(CR) systems and CR systems sense the spectrum of the licensed user by using a energy detection method. Threshold is determined in accordance with the constant false alarm rate(CFAR) algorithm for energy detection. The signal of licensed user is OFDM signal and the wireless channel between a licensed user and CR systems is modeled as Gaussian channel. From the simulation results, the cooperative spectrum sensing with distance based weight combining(DWC) and equal gain combing(EGC) methods shows higher spectrum sensing performance than single spectrum sensing does. And the detection probability performance with the DWC is higher than that with the EGC.