By using nonequilibrium Green's functions in combination with the first principles density functional theory, for the similar right triangle graphene devices as the research object, we take the zigzag graphene as electrodes, to investigate the B(N) doping and B-N co-doping effect, i.e. mainly the influence of doping on the transport properties of similar right triangle graphene devices, as well as the asymmetric doping effect on the rectifying behaviors in similar right triangle graphene devices. Calculated results show that the system conductivity is increased when the vertex carbon atom of a similar right triangle graphene is substituted by a boron or nitrogen atom, and a novel rectifying effect appears. The rectification behavior can be observed because of an asymmetric movement on the molecular-level in B(N) doping in the similar right triangle graphene devices under positive and negative biases and the asymmetry in the spatial distribution of the frontier orbitals. Most importantly, when the vertex carbon atoms of the right and left similar right triangle graphenes are simultaneously doped with boron and nitrogen atoms, the rectifying effect of the system is significantly enhanced and appears also a negative differential resistance effect.