Abstract: A physical problem of cyclotron equilibrium orbit was changed into a mathematical problem of solving the minimum value of the objective function by introducing the objective function which describes the orbit closing degree, and the optimal solution of the objective function was found out by using the simplex method so that the problem of the equilibrium orbit was solved. The method can be used to solve the corresponding equilibrium orbit only if any two of initial energy, initial azimuth, initial radius and initial radial momentum are given.