In this work, a graphene (GR)/MoS2/GR selector was proposed based on first principle calculations. First, MoS2 was chosen as the resistive switching layer due to its high carrier mobility and was doped with nine kinds of dopants. Semiconductor characteristics were still maintained with P, Si, and Ti doping, while the others showed semimetallic properties. Then, heterostructures were built between metal GR and MoSX (X = S, P, Si, Ti), and the conductivities of MoSSi and MoSTi were obviously improved with the GR electrode through analysis of the impurity orbital contribution to the band energy. The plane average electrostatic potential and the charge density difference show that the Schottky barrier height and width of the GR/MoSSi interface were the smallest and that the intensity of the built-in electric field was better than that of GR/MoS2 and GR/MoSTi. Finally, GR/MoSX(X = S, Si, Ti)/GR selectors were proposed, and the electronic transmission shows that the ON-state current (I-on) and nonlinear coefficient of the GR/MoSSi/GR selector were increased by two and three orders of magnitude, respectively, and the threshold voltage (V-th) was reduced by approximately 1 V, which can better suppress the leakage current in a one-selector one-RRAM cross array. This work may be instructive and valuable for the design and optimization of GR/MoS2/GR selectors.