The control design method for a class of non-strict feedback nonlinear systems is studied in this brief considering uncertain nonlinearities and unknown non-symmetrical input dead-zone. Combining with the finite-time command filtered backstepping (FCFB) technique, a novel finite-time adaptive control approach is proposed in which a neural network-based methodology is adopted to cope with the uncertain nonlinearities in the non-strict feedback form. The input dead-zone model is transformed into a simple linear system with unknown gain and bounded disturbance which is estimated by an adaptive factor. Using the finite-time Lyapunov theory, the system convergence is proved. And the effectiveness of the proposed control scheme is verified through comparative numerical simulations.