An arbitrary two-position north finder based on ring laser gyro was introduced. It can save the time of north finder to a certain extent. The solver formula of north finder in the whole attitude was derived. In order to improve the accuracy of north finder, the impact of the various errors including the drift of gyro, system circumference error and position transposition error on the accuracy of the arbitrary two-position north finder was analyzed theoretically, and the mathematical model of errors were established, and the method of reducing the error was proposed. Simulation result indicates that the position transformation under the level state bringing error of north finder is a constant, and is half of the position transformation. In order to ensure an enough high accuracy of north seeking, it requires the corner μ≥40° and the latitude φ≤70° of north finder in the course. The results of north finder further validate the correctness of the simulation results, consistent with the theoretical analysis.