In this paper, a new method for robust local polynomial regression (LPR) using M-estimator with adaptive bandwidth is proposed. This is motivated by the limitation of traditional LPR in detecting and removing impulsive noise or outlies. By using M-estimation technique and the intersection of confidence intervals (ICI) rule for choosing an adaptive local bandwidth, a robust LPR algorithm is developed. Simulation results show that the new M-estimation-based LPR performs considerably better than the traditional LS-based method in removing the impulsive noise as well as preserving the jump discontinuities, which are frequently found in image and video processing.