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In this paper, a generalized polyphase (GP) structure based design method for Mth-band FIR filters is presented. Based on the ideal frequency response of Mth-band filters, a closed-form frequency specification for the constituent filters is derived. Thus, the design problem of an original large-tap FIR filter is simplified to that of the constituent filters of significantly reduced length. In the meantime, the time-domain interpolation constraint can easily be satisfied by leaving one constituent filter as a function of other constituent filters designed. Using the proposed approach, an interpolation filter is designed and applied to image interpolation. Simulation results show that the designed Mth-band filter gives a superior interpolation performance in comparison to the commonly used cubic spline interpolation scheme.