In this paper, a new algorithm for non-uniformity correction of infrared focal plane arrays based on neural network and bi-exponential filter is proposed. Due to the edge preserving property of bi-exponential filter, the algorithm can estimate the gain and bias coefficients at the strong edge more accurately, thereby suppressing the ghosting effect. In order to suppress the blurring effect, a motion detection is carried out before the correction coefficients are updated. A motion evaluation index based on the L1 norm of the temporal variation of the image and the image roughness is designed to improve the accuracy of motion detection. Moreover, an adaptive learning rate calculation method is proposed, which makes the learning rate larger in the image smoothing region and smaller in the edge region. This results in a faster convergence in a uniform region of the image , and it is not easy to cause a correction coefficients estimation error in the edge region. Several infrared image sequences are used to verify the performance of the proposed algorithm. The results indicate that the proposed method can not only preserve the details of the image, but also reduce the non-uniformity. Besides, it has a good inhibitory effect on the phenomenon of ”ghosting” and ”blurring”.