In this paper, we propose an efficient successive interference cancellation (SIC) method in direct sequence code division multiple access (DS-CDMA) system using neural network (NN). Neural network is used here to estimate the amplitudes of different users signals under frequency selective Rayleigh fading channel. The correlation values between the received signal and the signature /spreading waveforms for different users are given as the inputs to a NN and the output acts as an estimation of corresponding user's signal amplitude. A closed mathematical form of joint probability of error (JPOE) is developed to determine the number of active users needs to be canceled to achieve a desired bit error rate (BER) value. Simulation results strongly support the mathematical results. Mathematical analysis shows that better performance results can be achieved through large change in weight up-gradation (w) for the strong users with a particular change in learning rate (η). Performance of the SIC system has been studied for initial wrong ordering of a couple of pairs of interfering users based on the correlation values. Simulation results show that BER performance is better when users are ordered based on signal to interference ratio (SIR) values rather than correlation values.