Recent studies of high quality, high resolution traffic measurements have revealed that network traffic appears to be statistically self similar. Contrary to the common belief, aggregating self-similar traffic streams can actually intensify rather than diminish burstiness. Thus, traffic prediction plays an important role in network management. In this paper, Least Mean Kurtosis (LMK), which uses the negated kurtosis of the error signal as the cost function, is proposed to predict the self similar traffic. Simulation results show that the prediction performance is improved greatly over the Least Mean Square (LMS) algorithm.