High contact resistance between TMDs and metals has been identified as an outstanding issue. TMDs tend to form a substantial Schottky barrier (SB) with commonly used metals. Air-stable graphene electrodes stacked on the WSe₂ by transfer technique have been reported. However, unipolar conduction has not been achieved in FETs based on TMD materials and graphene electrodes. Here we report a synthetic process to directly grow WSe₂ monolayers along the edge of patterned few-layered graphene, forming the lateral heterojunction between the graphene and monolayer WSe₂. The few-layered WSe₂ bridges the few-layer graphene and monolayer WSe₂, and an interpenetrating layered structure is formed between graphene and WSe₂. As a result, the WSe₂ monolayer channel and the junction to the graphene can be formed at the same time by the synthesis method, where graphene serves as source and drain. Graphene is in-situ heavily p-doped by H₂ with covent bond during WSe₂ growing process. Such a unique junction structure leads to a barrier less ohmic contact between doped graphene and WSe₂. Unipolar WSe₂ PFET with laterally contacted p-doped graphene source/drain (p-G/WSe₂ PFET) can be achieved for the first time. With Pd contacted source/drain metal, the unipolar PFET perform Ion/Ioff > 10⁵ and field effect mobility ~20 cm2/Vˑs. Moreover we can still have unipolar PFET with Ti source/drain metal exceeds 10³ Ion/Ioff ratio even Ti work function is low (4.3 eV)  and close to the conduction band edge of WSe₂ (electron affinity of WSe₂~ 4.03 eV).