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By performing first-principle quantum transport calculations, we investigate the effects of connected position and B/N doping on the transport properties of a single cruciform diamine molecule connected to zigzag graphene nanoribbon leads. The negative differential resistance behaviors are found in I V characteristics of the undoped molecular device. The peak-to-valley current ratio can be modulated obviously by changing the connected position. Then, we find the B/N doped effects are sensitive to doping site in the connected region. The replacement of B/N atom on R1 (carbon atom in connected region close to the zigzag graphene nanoribbon) seldom affects the transmission spectrum around Fermi level. But, the replacement of B/N atom on R2 (carbon atom in connected region close to the molecule) can raise the transmission coefficient around Fermi level markedly leading to the large growth of the current at the low biases. In addition, the replacement of N atom on R2 can induce a negative differential resistance behavior in I V curve at low bias region. [ABSTRACT FROM AUTHOR]