The design of an immersion and invariance (I&I) based composite adaptive control for a class of uncertain nonlinear systems is presented in this paper. The key feature of this control scheme lies in the construction of the novel adaptive laws, aiming to address both parametric and non-parametric uncertainties simultaneously. Composite adaptive laws, which are driven by both the information of tracking error and prediction error, are first proposed using I&I theory for the estimations of parametric uncertainties. Then the technique of σ-modification is used to guarantee the stability in the presence of non-parametric uncertainties. Stability analysis is presented using the Lyapunov theory. Improved performance of the proposed control scheme is observed via numerical simulations.