van der Waals (vdW) heterostructures generated by stacking of graphene with other two-dimensional (2D) crystalline sheets have produced a new class of "designer" materials which shows great promise for nanoscience and nanotechnology. However, the 2D sheets are obtained either from nature or synthesized by high-energy procedures, which preclude the design of their structures as well as properties from molecular design on demand. Here, we introduced a rationally designed 2D polymer (one-monomer unit thick, freestanding network composed of periodically linked monomers) as a component for heterostructure construction, and created a 2D polymer-graphene heterostructure. The heterostructure has a high chemical stability, and could be thermally stable up to 400 °C. In the heterostructure, the 2D polymer doped graphene without changing its intrinsic structure, leading to the enhancement of its electric conductivity by a factor of ∼2.5. This piece of work opens the door to tune the properties of graphene heterostructures with rational design for specific applications.