Abstract: Sigmoid function based on the logarithm operation is often used as the threshold function of neural network mapping variables between zero and one. In order to study its high speed, high precision, low power consumption, by logarithm operation for the realization of the principle, we do the research and then realize its function for the sigmoid function. We also do simple design verification through the SystemVerilog simulation platform, and summarize performance indicators of the sigmoid function on rate, precision, power consumption and so on by comparing the output of the simulation platform with the output of design. Results show that the designs of the sigmoid function on rate are improved, a functional operation needing seven clock cycles (frequency 200 MHZ), a slight increase on the precision. Hardware power consumption has been reduced.