Seismic data interpolation is a highly ill-posed problem. Therefore, designing an appropriate regulating method, aiming to reduce multi-solutions, is of utmost importance. Sparse and low-rank priors or constraints, which consider certain kinds of redundant data structures from different viewpoints, are widely used to constrain recovered seismic data to achieve a better fit. Considering that additional information enables us to obtain more accurate reconstructions, we formulated a seismic data interpolation model with irregular missing traces as a joint sparse and low-rank matrix approximation problem. The result is a solution that fits the given data, while simultaneously being sparse and low-rank. Subsequently, an efficient alternating algorithm is developed to solve the proposed objective function. Our proposed model called joint sparse and low-rank priors (JSLRP) model performs better on synthetic and field 3-D seismic data when compared to the classic low-rank methods, such as multichannel singular spectrum analysis (MSSA) and damped MSSA.