Abstract: The rational approximation of a fractional order system usually has some disadvantages: the order of the rational transfer function is high, the approximating precision is low, and the optimization speed is too slow. We propose a method of approximating the fractional order system using a lower order rational transfer function based on error minimum theory in the frequency domain. The method transforms the calculation of the minimum error between the fractional order system and its rational approximation function into a linear programming problem, thus avoiding having to solve a system of equations and nonlinear problems. Simulation results show that the rational approximation function constructed by the proposed method can achieve a better approximation effect with lower order in the whole frequency range of interest compared with the Charef and Oustaloup methods. The proposed method can apply to systems with fractional power poles and general fractional order systems composed of fractional order differential operators. The proposed method reduces the computation complexity and improves the optimization speed.