AbstractIn this paper, the adaptive multi‐dimensional Taylor network (MTN) control problem is investigated for nonlinear stochastic systems with full state time‐varying constraints and the finite‐time output constraint. By combining the MTN‐based approximation method and the adaptive backstepping control method, a novel adaptive MTN control scheme is provided by constructing the time‐varying barrier Lyapunov function (TVBLF). To implement the finite‐time output constraint, the finite‐time performance function (FTPF) is introduced in the control scheme. The proposed scheme can ensure that the tracking error finally converges to a small neighborhood of the origin in the finite‐time and all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB) in probability. Finally, two simulation examples are presented to show the effectiveness of the provided control scheme.