Superconductors with a van der Waals (vdW) structure have attracted a considerable interest because of the possibility for truly two-dimensional (2D) superconducting systems. We recently reported NaSn2As2 as a novel vdW-type superconductor with transition temperature (Tc) of 1.3 K. Herein, we present the crystal structure and superconductivity of new material Na1-xSn2P2 with Tc = 2.0 K. Its crystal structure consists of two layers of a buckled honeycomb network of SnP, bound by the vdW forces and separated by Na ions, as similar to that of NaSn2As2. Amount of Na deficiency (x) was estimated to be 0.074(18) using synchrotron X-ray diffraction. Bulk nature of superconductivity was confirmed by the measurements of electrical resistivity, magnetic susceptibility, and specific heat. First-principles calculation using density functional theory shows that Na1-xSn2P2 and NaSn2As2 have comparable electronic structure, suggesting higher Tc of Na1-xSn2P2 resulted from increased density of states at the Fermi level due to Na deficiency. Because there are various structural analogues with tin-pnictide (SnPn) conducting layers, our results indicate that SnPn-based layered compounds can be categorized into a novel family of vdW-type superconductors, providing a new platform for studies on physics and chemistry of low-dimensional superconductors.