An L-parallel coprime array is designed and an Off-grid sparse learning via iterative minimization (OGSLIM) algorithm is proposed in order to improve the performance of Two-dimensional direction-of-arrival (2-D DOA) estimation. The L-parallel coprime array consists of two parts, one is a parallel coprime array and the other one is a linear coprime array perpendicular to the parallel coprime array. The OGSLIM algorithm is based on sparse Bayesian framework and can learn the offi-grid parameter. Theory analysis and simulation results demonstrate that 2-D DOA estimation using OGSLIM algorithm with L-parallel coprime array can lead to higher estimation accuracy and resolution, it also fits to the underdetermined signals and correlated signals.