Rotating modulation for Strap-down Inertial Navigation System (SINS) is an auto-correction technology in nature. In order to study the error compensation principle of single-axis rotary SINS, an attitude error model is deduced by the quaternion differential equation, which is consist with the one deduced by direction cosine matrix differential equation. The general system error models and error propagation equation on stationary base are established, and the modulation forms of inertial device errors are analyzed, which provides a reference for rotary scheme design. Simulation is made to the influence of gyro constant drift, scale factor error and setting error based on single-axis continuous rotation on navigation error. Theoretical analysis and simulation results show that continuous rotation of inertial measurement unit can effectively restrain the navigation error.