Abstract: The ship rolling prevents a gyroscope from reliably measuring the angular velocity of the earth's rotation (Ω). Consequently,the strapdown compass system based on fiber optic gyroscopes (FOG) cannot compute the heading of the carrier based on the outputs of gyroscopes and the accelerometers. To address this issue, a new north finding algorithm was proposed. By taking the inertial frame as the reference coordinate frame, this algorithm established the transitional inertial frame and the initial-time strapdown compass body inertial frame. The direction of vector Ω was then calculated according to the projection of the accelerometer sensitive to grivity in the initial-time body inertial frame. And this in turn recovers the true north of geographic direction. The proposed north finding algorithm consists of three steps. It established the initial-time body inertial frame. Then it obtained a stable level frame via the initial-time body frame and the outputs of gyroscope and accelerometer. By projecting the output of accelerometer from the strapdown compass body frame to the initial-time body inertial frame, the direction of vector Ω was calculated by the space circle fitting method. Then the true north was recovered by projecting the vector parallel with Ω from the initial-time body inertial frame to the stable level frame. The simulation result shows that the error of azimuth can be reduced to as low as 0.23°(1σ) .