We investigate the eleetronic transport properties of dipyrimidinyl-diphenyl sandwiched between two armchair graphene nanoribbon electrodes using the nonequilibrium Green function formalism combined with a firstprinciples method based on density functional theory. Among the three models M1-M3, Ml is not doped with a heteroatom. In the left parts of M2 and M3, nitrogen atoms are doped at two edges of the nanoribbon. In the right parts, nitrogen atoms are doped at one center and at the edges of M2 and M3, respectively. Comparisons of M1, M2 and M3 show obvious rectifying characteristics, and the maximum rectification ratios are up to 42.9 in M2. The results show that the rectifying behavior is strongly dependent on the doping position of electrodes. A higher rectifhcation ratio can be found in the dipyrimidinyl-diphenyl molecular device with asymmetric doping of left and right electrodes, which suggests that this system has a broader application in future logic and memory devices. We investigate the eleetronic transport properties of dipyrimidinyl-diphenyl sandwiched between two armchair graphene nanoribbon electrodes using the nonequilibrium Green function formalism combined with a first principles method on density functional theory. Among the three models M1-M3, M1 is not doped with a heteroatom. In the left parts of M2 and M3, nitrogen atoms are doped at two edges of the nanoribbon. In the right parts, nitrogen atoms are doped at one center and at the edges of M2 and M3, respectively. Comparisons of M1, M2 and M3 show obvious that the rectifying behavior is strongly dependent on the doping position of electrodes. A higher rectification ratio can be found in the dipyrimidinyl-diphenyl molecular device with asymmetric doping of left and right electrodes, which suggests that this system has a broader application in future logic and memory devices.