Soliton molecules, referred to as closely bounded solitons, have recently attracted considerable interest in both fundamental nonlinear physics research and refreshed application promises. To date, extensive efforts have been made on the generation of quadratic soliton molecules. These are soliton molecules whose formation exclusively involves second-order dispersion and Kerr nonlinearity. Here, for the first time, we demonstrate the realization of various third-order dispersion-supported soliton molecules, including vector dark–anti-dark solitons, vector anti-dark solitons, and vector anti-dark soliton molecules formed in a fiber laser with net cavity dispersion near the zero-group-velocity-dispersion point. High-order dispersion could greatly alter the internal soliton interaction within a soliton molecule. This finding could open exciting new avenues in soliton research.