Abstract Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system. In this study, we predicted the phase transition of the third-order Lovelock black hole using the winding numbers in complex analysis, and qualitatively validated this prediction by the generalized free energy. For the $7\le d\le12$-dimensional black holes in hyperbolic topology and the $7$-dimensional black hole in spherical topology, the winding number obtained is three which indicate that the system undergoes first-order and second-order phase transitions. For the $7<d<12$-dimensional black holes in spherical topology, the winding number is four, and two scenarios of phase transitions exist, one involving a purely second-order phase transition, and the other involving simultaneous first-order and second-order phase transitions. This result further deepens the research on exploring black hole phase transitions using the complex analysis.