The thermal transport properties by phonons in zigzag graphene nanoribbons with structural defects are investigated by using nonequilibrium phonon Green's function formalism. We find that the combined effect of the edge and local defect plays an important role in determining the thermal transport properties. In the limit T → 0, the thermal conductance approaches the universal quantum value 3κ(0)(κ(0) = π(2)k(B)(2)T/3h) even when structural defects are presented in graphene nanoribbons. The thermal transport shows a noticeable transformation from quantum to classical features with increasing temperature in the system. A suggestion to tune the thermal conductance by modulating structural defects and the ribbon width in graphene nanoribbons is presented.