In this paper, an output feedback finite-time controller based on a finite-time stable observer is developed for a bioreactor system. The observer is proposed to estimate the biomass concentration in finite time. Based on the estimation of the biomass concentration, an output feedback controller is designed to track the reference signal in finite time. A Lyapunov function is constructed to prove that the observer is a finite-time stable observer. The finite-time stability results for cascaded systems are employed to prove that the closed-loop system satisfies the finite-time stability. Thus, the observer and the controller can be designed separately, both with finite-time convergence. Numerical simulation results demonstrate the effectiveness of the method.