This paper deals with two new methods, based on k-NN algorithm, for fault detection and classification in distance protection. In these methods, by finding the distance between each sample and its fifth nearest neighbor in a predefault window, the fault occurrence time and the faulty phases are determined. The maximum value of the distances in case of detection and classification procedures is compared with pre-defined threshold values. The main advantages of these methods are: simplicity, low calculation burden, acceptable accuracy, and speed. The performance of the proposed scheme is tested on a typical system in MATLAB Simulink. Various possible fault types in different fault resistances, fault inception angles, fault locations, short circuit levels, X/R ratios, source load angles are simulated. In addition, the performance of similar six well-known classification techniques is compared with the proposed classification method using plenty of simulation data.