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This paper addresses a robust adaptive control problem of non-square nonlinear systems with unmeasurable states. The systems are assumed to be multi-input/multi-output subject to dynamical uncertainties and external disturbances. The approach is studied for two cases, i.e., underactuated and over-actuated nonlinear systems. The new observer does not need to satisfy the SPR conditions. Moreover, a constant full-rank matrix with an adaptive gain is used to approximate the unknown gain matrix. Therefore, the proposed controller’s structure simplifies its implementation. The unknown nonlinearity is estimated neural networks. Stability of the closed-loop system is proved using Lyapunov analysis. The feasibility of the proposed approach is validated by simulation examples.