Based on the principle of rotation modulation, a method of fast northseeking of partial period is proposed. First, an output model of northseeking is constructed. Then, threeparameter sine wave fit is introduced, and the CramerRao lower bound for parameters estimation of sine wave is derived. At the last, a fast northseeking experiment of fiber optic gyroscope is designed. It is shown that the fewer the data of partial period are, the lower the accuracy of sine parameter estimation is. It is also concluded that the northseeking accuracies of 1/3 period and 1 period are 0.3° and 0.009° respectively by using the gyroscope. The method is valid to fast northseeking.