Two-dimensional (2D) magnetic materials have aroused tremendous interest due to the 2D confinement of magnetism and potential applications in spintronic and valleytronic devices. However, most of the currently 2D magnetic materials are achieved by the exfoliation from their bulks, of which the thickness and domain size are difficult to control, limiting the practical device applications. Here, we demonstrate the realization of thickness-tunable rhombohedral Cr2Se3 nanosheets on different substrates via the chemical vapor deposition route. The magnetic transition temperature at about 75 K is observed. Furthermore, van der Waals heterostructures consisting of Cr2Se3 nanosheets and monolayer WS2 are constructed. We observe the magnetic proximity effect in the heterostructures, which manifests the manipulation of the valley polarization in monolayer WS2. Our work contributes to the vapor growth and applications of 2D magnetic materials.