A synthesis filter for an MPEG audio decoder, and a decoding method thereof. The synthesis filter for an MPEG audio decoder includes a butterfly computation part which performs a butterfly computation with respect to an input MPEG audio subband sample by a predetermined unit, a matrix computation part which performs a matrix computation using a result of the butterfly computation, a first buffer which stores a result of the matrix computation according to a predetermined address, a window computation address generation part which generates first and second addresses with respect to the first buffer to use for each cycle of the window computation, a window computation part which outputs the matrix computation result stored to the first and second addresses to perform the window computation, and an output part which outputs a result of the window computation.