Combination of two dimensional graphene and semi-conducting molybdenum disulfide (MoS2) is of great interest for various electronic device applications. Here, we demonstrate fabrication of a hybridized structure with the chemical vapor deposited graphene and MoS2 crystals to configure a memory device. Elongated hexagonal and rhombus shaped MoS2 crystals are synthesized by sulfurization of thermally evaporated molybdenum oxide (MoO3) thin film. Scanning transmission electron microscope studies reveal atomic level structure of the synthesized high quality MoS2 crystals. In the prospect of a memory device fabrication, poly(methyl methacrylate) (PMMA) is used as an insulating dielectric material as well as a supporting layer to transfer the MoS2 crystals. In the fabricated device, PMMA-MoS2 and graphene layers act as the functional and electrode materials, respectively. Distinctive bistable electrical switching and nonvolatile rewritable memory effect is observed in the fabricated PMMA-MoS2/graphene heterostructure. The developed material system and demonstrated memory device fabrication can be significant for next generation data storage applications.