Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). Accurate and fast image reconstruction from non-Cartesian k-space data becomes a challenge and gains a lot of attention. Images provided by conventional direct reconstruction methods usually bear ringing, streaking, and other leakage artifacts caused by discontinuous structures. In this paper, we tackle these ... [Show full abstract] problems by analyzing the principal point spread function (PSF) of non-Cartesian reconstruction and propose a leakage reduction reconstruction scheme based on discontinuity subtraction. Data fidelity in k-space is enforced during each iteration. Multidimensional nonuniform fast Fourier transform (NUFFT) algorithms are utilized to simulate the k-space samples as well as to reconstruct images. The proposed method is compared to the direct reconstruction method on computer-simulated phantoms and physical scans. Non-Cartesian sampling trajectories including 2D spiral, 2D and 3D radial trajectories are studied. The proposed method is found useful on reducing artifacts due to high image discontinuities. It also improves the quality of images reconstructed from undersampled data.