A modified compartmentalized reactor where the inflow of substrate and the outflow of product can be separately controlled was devised for studying self-sustained oscillations of an enzyme reaction. This reaction-diffusion system consists of a well-stirred reactor inserted between two membranes and reservoirs. By changing the characteristics of the two membranes, such as their thickness and permeability, the reactor inflow and outflow can be modulated. The reaction involved was a hydrolysis of N-a -benzoyl- L-arginine ethyl ester by papain, a proteolytic enzyme. The regions in the parameter space where self-sustained oscillations can be induced were determined via numerical simulation. The mechanism of the oscillations was also discussed. As a result, we found that with the appropriate parameters, the sizes of the regions for the modified compartmentalized reactor were larger than those for the former type. This shows the significance of the separate control of the reactor inflow and outflow. It is also suggested that this reactor system could be used as a model one for studying the dynamics of biological systems and for developing biomimetic devices.