This paper deals with the design of a generalized dynamic observer for a class of Nonlinear Parameter-Varying (NLPV) systems. The primary goal is to formulate a less conservative Linear Matrix Inequality (LMI) condition than the existing ones, ensuring the exponential stability of the error dynamics in the proposed observer. Through the incorporation of the reformulated Lipschitz property, Young’s inequalities and a generalized matrix multiplier, two new LMI conditions are established. Due to the deliberate use of these mathematical tools, the obtained LMI conditions contain a larger number of decision variables than existing LMI conditions. As a result, these LMIs have enhanced feasibility than the one presented in the literature. The effectiveness of the newly designed LMI-based generalized dynamic observer is highlighted through a numerical example.