Cracking gas compressor is usually a centrifugal compressor. The information on the performance of a centrifugal compressor under all conditions is not available, which restricts the operation optimization for compressor. To solve this problem, two back propagation (BP) neural networks were introduced to model the performance of a compressor by using the data provided by manufacturer. The input data of the model under other conditions should be corrected according to the similarity theory. The method was used to optimize the system of a cracking gas compressor by embedding the compressor performance model into the ASPEN PLUS model of compressor. The result shows that it is an effective method to optimize the compressor system.