Multi-layered materials provide fascinating platforms to realize various functional properties, possibly leading to future electronic devices controlled by external fields. In particular, layered magnets coupled with conducting layers have been extensively studied recently for possible control of their transport properties via the spin structure. Successful control of quantum-transport properties in the materials with antiferromagnetic (AFM) layers, so-called natural spin-valve structure, has been reported for the Dirac Fermion and topological/axion materials. However, a bulk crystal in which magnetic and superconducting layers are alternately stacked has not been realized until now, and the search for functional properties in it is an interesting yet unexplored field in material science. Here, we discover superconductivity providing such an ideal platform in EuSn2As2 with the van der Waals stacking of magnetic Eu layers and superconducting Sn-As layers, and present the first demonstration of a natural spin-valve effect on the superconducting current. Below the superconducting transition temperature (Tc), the electrical resistivity becomes zero in the in-plane direction. In contrast, it, surprisingly, remains finite down to the lowest temperature in the out-of-plane direction, mostly due to the structure of intrinsic magnetic Josephson junctions in EuSn2As2. The magnetic order of the Eu layers (or natural spin-valve) is observed to be extremely soft, allowing one to easy control of the out-of-plane to in-plane resistivities ratio from 1 to infinity by weak external magnetic fields. The concept of multi-functional materials with stacked magnetic-superconducting layers will open a new pathway to develop novel spintronic devices with magnetically controllable superconductivity.