Proton Exchange Membrane Fuel Cell (PEMFC) which is an efficient renewable energy system has usage area in home and industrial applications. Since the generated voltage from PEMFC is low, the output voltage of it can be increased by using a boost converter. The boost converter fed by PEMFC can normally be controlled by the classical PI controller which parameters (K-P, K-i) are constant and do not depend on the circuit parameters. Therefore, these coefficients are non-adaptive at variable load situations. In this study, an improved controller is obtained by regulating the PI controller according to Lyapunov stability theorem. Then, this improved Lyapunov based PI controller is proposed for PEMFC based boost converter. In the proposed method, K-P and K-i parameters vary adaptively depending on the circuit parameters. Thus, the system works more stable and settling time of system's output voltage signal decreased compared to classical PI controller. The proposed method has been successfully tested in Matlab/Simulink environment.