In this paper, the finite time speed regulation problem is investigated for a dual three-phase hybrid excitation synchronous machine (DTP-HESM) without a torque meter. The electromagnetic torque estimation required in the current coordinative strategy is obtained through the disturbance estimation technology. This method increases fault tolerance and reduces the cost as well as complexity of the DTP-HESM system. In contrast to the existing controllers in the speed loop, the non-singular terminal sliding mode control method is adopted to ensure the finite-time convergence of speed tracking in the whole speed region. To achieve better dynamic performance in the presence of lumped disturbances, including unknown load torque and unmodeled dynamics, the disturbance estimations are introduced into the sliding mode variable to establish a composite speed regulating controller. Simulations and experiments are carried out to validate the feasibility and effectiveness of the proposed control scheme.