Low Probability of Intercept(LPI) periodic sequences with low autocorrelation sidelobes are desired in many application, especially in LPI radar systems. In this letter, we propose an algorithm to design LPI periodic sequences that counteract cyclic spectrum analysis while maintaining low autocorrelation sidelobe characteristics. We begin by simplifying the weighted cyclic frequency sidelobe (WCFS) level into a quadratic form, and then minimize the WCFS level to better approximate the cyclic spectrum of Gaussian white noise. To ensure the accuracy and detection capability of the solution, we introduce a Peak-to-Average Power Ratio (PAPR) condition for the power spectrum, which is subsequently transformed into a frequency constraint. Finally, leveraging the cyclic algorithm(CA), we introduce a monotonic WCFS minimization algorithm to address the aforementioned optimization problem. The simulation results presented in this letter demonstrate the correctness and effectiveness of our proposed algorithm.