By using nonequilibrium Green’s function method, the thermal transport properties of L-shaped graphene nano-junctions consisting of a semi-infinite armchair-edged nanoribbon and a semi-infinite zigzag-edged nanoribbon were studied. It is shown that the thermal conductance of the L-shaped graphene nano-junctions depends on the included angles and the widths of the graphene nanoribbons. As the angle of L-shaped graphene nano-junctions increases from 30° to 90° and further to 150°, the thermal conductance obviously increases. For the right-angle L-shape graphene nano-junction, the thermal conductance undergoes a transition with the increasing of the widths of the armchair nanoribbons. The thermal conductance decreases at low temperature region and increases at high temperature region. Meanwhile the thermal conductance of L-shape graphene nano-junction with included angle 150° decreases by increasing the widths of zigzag-edged nanoribbons in both low and high temperature regions. These thermal transport phenomena can be reasonably explained by analyzing the phonon transmission coefficient. We illustrate the mechanisms of thermal transport for different L-shaped graphene nano-junctions. The results provide significant physical models and theoretical basis for designing the thermal devices based on the graphene nano-junctions.