Introducing variable cross-section structures to graphene is considered to be an important method for producing thermal rectification (TR). In our work, non-equilibrium molecular dynamics simulations of variable cross-section graphene with nanojunctions were conducted, and their effects on thermal-transport properties were systematically studied. The results show that the introduction of nanojunctions can induce local phonon resonance effects, and the type of nanojunctions can influence these effects. The use of inclined nanojunctions can weaken local resonance compared to the use of straight nanojunctions. According to the results, the local resonance can be improved by increasing the length of the inclined nanojunctions within a certain range. However, beyond a specific length, the local resonance weakens. Finally, the directional difference in the phonon spectral heat flux and the directional mismatch of the dispersion curves are used to explain the TR phenomenon in the model. It is also found that low-frequency phonons play a key role in the TR phenomenon through the phonon density of states. This work provides guidance for designing local phonon resonance-based thermal rectifiers by tailoring graphene devices.