The high cost and large volume of three-axis high-precision optical gyroscope have hindered the widespread application of the gyroscope-based north-finding technology in the field of mobile robotics. In response to this issue, a method for indoor mobile robot north-finding based on a single-axis optical gyroscope and Micro-Electro-Mechanical System ( MEMS) Inertial Measurement Unit is proposed. This method achieves or approaches the heading accuracy of three-axis optical gyroscope while reducing costs and volume by approximately two-thirds. When the mobile robot is stationary at its initial position, two potential heading angles are obtained by combining the output of the single-axis optical gyroscope with the output of a MEMS three-axis accelerometer. Similarly, two potential heading angles at the second position are obtained in the same manner. By subtracting the heading angles at the two positions, four potential heading change values are derived. A unique heading angle for the second position is determined by comparing these values with the heading change value obtained from the MEMS strapdown inertial navigation system. Error analysis shows that the proposed method achieves a heading accuracy close to three-axis optical gyroscopes, especially when the heading angles are near 90° and 270°. Experimental results from on-vehicle tests confirm the effectiveness of the proposed method. Keywords:gyroscope-based north-finding; inertial navigation; single-axis optical gyroscope; M