An adaptive neural network consensus control algorithm is proposed for a class of non-strict feedback stochastic multi-agent systems with unknown input saturations and output dead zones. To solve the problem of asymmetric input saturations, an auxiliary system with the same order as the considered agent is constructed. Based on the framework of the backstepping method and the auxiliary system, neural networks are utilized to approximate the unknown nonlinear functions of multi-agent systems, and the Nussbaum function is introduced to compensate the negative effect of output dead zones. Moreover, the dynamic surface control technique is employed to avoid the problem of “explosion of complexity”. According to the Lyapunov stability theory, it is strictly proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in probability. Finally, simulation results are provided to verify the effectiveness of the proposed control algorithm.