We propose and demonstrate a momentum filter for atomic gas-based on a designed Talbot–Lau interferometer. It consists of two identical optical standing-wave pulses separated by a delay equal to odd multiples of the half Talbot time. The one-dimensional momentum width along the long direction of a cigar-shaped condensate is rapidly and greatly purified to a minimum, which corresponds to the ground state energy of the confining trap in our experiment. We find good agreement between theoretical analysis and experimental results. The filter is also effective for non-condensed cold atoms and could be applied widely.