To provide a gyro compass for the use of a high speed ship, in a gyro compass of the type having north-seeking means which is applied to support a gyro sphere or gyro case immersed in a liquid in a tank, a substantially first-order lag filter is provided in an azimuth follow-up loop or a damping loop, the substantially first-order lag filter having a time constant T.sub.F which is approximately equal to a ratio C/k.sub.T of the viscosity torque coefficient C to the twisting torque coefficient k.sub.T of the torque produced between the tank and the gyro case. A speed error correcting means has a substantially first-order lag filter having a time constant which is approximately equal to that of the north-seeking means, and is applied to correct the output of azimuth indicator by a speed error correcting angle through the substantially first-order lag filter.