In this paper, an exchange algorithm is proposed to design sparse linear phase finite impulse response (FIR) filters with reduced effective length. The sparse FIR filter design problem is formally an l₀-norm minimization problem. This original design problem is re-formulated by encoding the filter coefficients using a binary encoding vector, which represents the locations of the zero and non-zero filter coefficients. An iterative 0-1 exchange process with proper direction control is proposed to propel the minimax approximation error toward the specified upper bound of error for sparsity maximization. The effective length is optimized with a lower priority than sparsity in the proposed algorithm. Simulation results show that the proposed algorithm is superior to the existing algorithms in terms of both sparsity and/or effective length in most cases.