In order to attain high precision positioning and navigation results with GPS, cycle slips must be correctly detected and repaired at the data preprocessing stage. Based on the characteristics of cycle slip we analyzed, a novel two-stage method was developed. Firstly, the wavelet multi-resolution analysis (MRA) is carried out and then the location of the cycle slip can be detected by ascertaining the point of modulus maximal value of the wavelet coefficients since the cycle slip can be regarded as the singular point of the signal. Secondly, two prediction models based on artificial neural network (ANN) are established respectively at the both side of the cycle slip. The actual number of cycle slip can be determined through comparing the difference of forecasting data of the two prediction models. Finally, test results are presented to demonstrate the feasibility and validity of the method.