An adaptive parameter estimation algorithm for a class of biochemical processes expressed by a nonlinearly parametrized Monod's growth kinetics model is presented. Contrary, to conventional least-square or gradient-ope identification techniques, the proposed parameter estimation algorithm is developed based on Lyapunov's stability theory. A novel class of parameter-dependent Lyapunov functions is utilized to remove the difficulty associated with estimating the unknown parameters that appear nonlinearly. A persistence of excitation (PE) condition is investigated to guarantee the convergence of the estimation scheme. Simulations are provided to verify the effectiveness of the new approach and the theoretical discussion.