This article proposes a new method for sensitivity analysis of machine tool position errors. Firstly, the position error model of five axis gantry machine tool is formulated, which is based on the multi-body theory and homogeneous transformation matrix. Secondly, the geometric error parameters related to the position are characterized by the truncated Fourier technique. The sensitive value of each error parameter to position error can be expressed as its Fourier amplitude square. After normalization, the key geometric error parameters are the 2nd, 3rd, 8th, 15th and 26th errors. Compared with the traditional Sobol method, the simulation results show that the key geometric errors identified by the two sensitivity analysis methods are the same and the sensitivity values are similar. In addition, the calculation efficiency of sensitivity analysis of the proposed method is better than that of traditional Sobol method. Finally, to verify the validity of key geometric errors, a compensation experiment on key geometric errors of machine tools is proposed. Experimental results show that the machining accuracy of the machine tool is improved by 48% after the key geometric errors are compensated. Therefore, the sensitivity analysis method of machine tool position error in this article is feasible and effective.