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Continuity, real-time, and accuracy are the key technical indexes of evaluating comprehensive performance of a strapdown inertial navigation system (SINS). However, Schuler, Foucault, and Earth periodic oscillation errors significantly cut down the real-time accuracy of SINS. A method for oscillation error restriction of SINS based on forecasted time series is proposed by analyzing the characteristics of periodic oscillation errors. The innovative method gains multiple sets of navigation solutions with different phase delays in virtue of the forecasted time series acquired through the measurement data of the inertial measurement unit (IMU). With the help of curve-fitting based on least square method, the forecasted time series is obtained while distinguishing and removing small angular motion interference in the process of initial alignment. Finally, the periodic oscillation errors are restricted on account of the principle of eliminating the periodic oscillation signal with a half-wave delay by mean value. Simulation and test results show that the method has good performance in restricting the Schuler, Foucault, and Earth oscillation errors of SINS.