Abstract: A high precision numerical simulation algorithm is the key of simulation design, which is a powerful tool to study the characteristics of the movement of ions in ion trap and the optimization of ion trap mass spectrometer. Two numerical methods based on fourth order and fifth-order Runge-Kutta algorithm to solve Mathieu equation were discussed. By using the Matrix Laboratory (Matlab) programming, the research studied the impacts of different parameters, such as calculation accuracy, initial value of position and time step, on the calculation results of ion trajectories. The results show that the fifth order Runge-Kutta algorithm can meet the requirements of simulation and achieve high precision ion trajectory simulation.