This paper addresses adaptive observer design problem for joint estimation of the states and unknown parameters for a class of nonlinear systems which satisfying one-sided Lipschitz and quadratic inner bounded conditions. It’s shown that the stability of the proposed observer is related to finding solutions to a quadratic inequality consists of state and parameter errors. A coordinate transformation is used to reformulate this inequality as a linear matrix inequality (LMI). Sufficient conditions that ensure the existence of adaptive observer are expressed in forms of LMIs, which are easily tractable via standard software algorithms. If the proposed conditions are satisfied, then the state estimation errors are guaranteed to converge to zero asymptotically while, the convergence of the parameters is guaranteed when a persistence of excitation condition is held. The effectiveness of the proposed method is shown by simulation for the joint estimation of states and parameters of a numerical system.