A video encoding method includes subjecting an input video image to motion compensated temporal filtering using a motion compensated temporal filter to produce a low-pass filtered image, quantizing a transform coefficient of the low-pass filtered image, encoding a quantized transform coefficient, calculating a weight to be given to a low-pass filter coefficient of a low-pass filter of the motion compensated temporal filter according to coarseness of quantization and a magnitude of a motion compensated error, and controlling a high band stopping characteristic of the low-pass filter according to the low-pass filter coefficient weighted by the weight, wherein the controlling controls the high band stopping characteristic of the low-pass filter to provide a positive correlation with respect to the quantization parameter and provide a negative correlation with respect to the magnitude of the motion compensated error.