Based on finite-time stability approach, a terminal block backstepping control with perturbation estimation scheme is proposed in this paper for a class of multi-input systems with matched and mismatched perturbations to solve regulation problems. The design procedure of the proposed control scheme mainly contains two parts. The first part is the design of pseudo-control inputs, the second part is the design of control input functions. In order to eliminate the problem of explosion of complexity' and overcome the problem of singularity, a derivative estimation algorithm embedded in the controller is utilised to estimate the perturbations. The control efforts are capable of suppressing the mismatched perturbations in most cases effectively so that the controlled states are able to reach zero within finite time. A numerical example is also given for demonstrating the feasibility of the proposed control scheme.