This paper mainly studies the finite-time adaptive tracking control of a class of non-strict feedback stochastic nonlinear systems with input quantization and full-state constraints. First, the hyperbolic tangent function is used for nonlinear mapping, which eliminates the constraints of the full-state constraints and transforms the system into an unconstrained system. Second, a hysteresis quantizer is introduced to avoid the chattering and reduce the quantisation error in the quantized signal. Third, in order to achieve finite time control, a semi-global finite time stability criterion is proposed in the sense of probability, which speeds up the convergence speed of the system. On this basis, radial basis function neural networks are used to approximate the unknown nonlinear functions. Based on the dynamic surface control technology and the properties of the Gaussian function, adaptive control design is performed for the transformed non-strict feedback stochastic system. The designed controller can guarantee that all signals in the closed-loop system are semi-globally finite time stable in probability(SGFTSP). Simulation results show the effectiveness of the proposed control scheme.