This article proposes a novel multidimensional Taylor network (MTN)‐based adaptive finite‐time control approach for stochastic nonlinear systems with input saturation constraints. First, by introducing the hyperbolic tangent function, a piecewise smooth function is proposed to approximate the input saturation constraints, which can solve the problem caused by input saturation. Then, with the aid of MTN approximation theorem, a novel adaptive finite‐time control approach is proposed, which can guarantee that all signals of the closed‐loop system are semi‐globally finite‐time stability in probability (SGFTSP), the system output follows the given reference signal, meanwhile, the tracking error converges to a small neighborhood of the origin in finite‐time. Compared with the existing results, the proposed approach has the characteristics of simple structure and low calculation, which can achieve the satisfactory control performance with a reduced computational burden. In the end, the effectiveness of the proposed approach is validated by Lyapunov stability theory and two simulation experiments.