This paper proposes an improved cycle slip detection algorithm based on Newton interpolation to address the issue of the inability to correctly solve discontinuous epoch when detecting cycle slips using pseudo range phase combination method and traditional high order difference method. This algorithm incorporates the Newton interpolation algorithm in the traditional process of detecting cycle slips with high order differences, which can be applied to the discontinuous epoch observations formed after satellite signal losing lock. Moreover, the Newton interpolation algorithm is more concise in terms of computational complexity compared to the Lagrangian interpolation algorithm. After the new node is generated, only a slight deformation of the basic formula based on the difference table is needed. It improves the algorithm adaptability to large amounts of data. In the practical testing, the effect is good, and the simulation results show that the improved cycle slip algorithm can correctly detect cycle slips after data interruption recapture, and can be applied to relevant data preprocessing algorithms to reduce the impact of outliers on positioning accuracy.