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A novel suboptimal paradigm is developed to compute the power-efficient linear-phase nonequiripple notch filters based on the orthogonal matching pursuit (OMP) scheme and the Chebyshev window. The design procedure proceeds as follows: At each iteration, the OMP scheme is employed to compute an FIR notch filter, which is then refined with a predevised Chebyshev window to improve its performance. The iteration procedure stops when the refined filter meets the predevised design specifications. The simulation results show that the proposed OMP scheme could be used to compute power-efficient linear-phase notch FIR filters.