The position error of array antenna significantly deteriorates the gain and sidelobe of the array, which seriously hinders the realization of high performance of communication antenna for Internet of Things (IoT). Based on the sensitivity analysis theory, the sensitivity of the array radiation field with respect to the position of the antenna element is derived. Besides, a novel design method of position tolerance for array antenna is proposed and applied to a 20 × 20 planar array. Compared with the array designed by traditional method, the gain loss is basically the same (being 0.5 dB), while the peak sidelobe level is lowered by 1.937 dB ( = 0 ∘ )/1.586 dB ( = 90 ∘ ). Besides, the uncertainty analysis results show that the newly designed array has a much higher chance to achieve the desired performance, which fully demonstrates the innovation and effectiveness of the new method.