Minimum power distortionless response (MPDR) beamformer is a popular beamformer that minimizes its output power under the distortionless constraint. To improve the performance of the MPDR beamformer, a sparse distortionless beamformer has been proposed. It minimizes the ℓ1 norm of the output signal under the same constraint so that the output has sparse time-frequency representation. While the ℓ1-norm-based formulation is theoretically advantageous owing to its convexity, its practical performance might not be excellent because of the bias of the ℓ1 norm. To reduce the bias and improve the performance, we propose a sparse distortionless beamformer based on a nonconvex sparsity-inducing objective function. The proposed beamformer is performed via a heuristic application of a primal-dual splitting algorithm. The experiments showed that the proposed beamformer can achieve higher performance and is more robust against mismatch of the target direction.