The contact resistance at two-dimensional graphene/MoS2 lateral heterojunctions is theoretically studied, using first-principles simulations based on density functional theory and the nonequilibrium Green's function method. The computed contact resistance lies in the range of 102 to 104 Ω μm, depending on the contact edge symmetry (armchair or zigzag) and termination (Mo and/or S terminated). This large variation in the contact resistance arises from the variation in the interface barrier height, which is sensitive to the presence of polar C-Mo bonds or sulfur dangling bonds at the interface. These results highlight that the control of the edge symmetry and/or edge termination is crucial to achieve a low contact resistance (in the range of a few hundred ohms micrometer) at graphene/MoS2 lateral heterojunctions for 2D material-based field-effect devices.