A novel theoretical analysis was performed to regulate the oxygen concentration in water using a membrane contactor composed of nonporous hollow fibers. The governing ordinary differential equations were derived for the countercurrent flow of the feed water and the feed gas in a membrane contactor. The governing equations were regarded as a two point boundary value problem. The nonlinear ordinary differential equations were simultaneously solved using a finite difference method. The computer program was coded in Fortran language using the Compaq Visual Fortran Software. It was found that the concentration of oxygen dissolved in water increases from 28.9 to 64.3 ppm as the area of the membrane increases from 1.24 to 3.73 m2 at the given typical operating condition: the flow rate of the feed gas is kept to be 1.0 L/min; its pressure is maintained to be 4 atm; the flow rate of the water is 15 L/min. It is observed that the concentration of oxygen increases from 48.2 to 56.2 ppm as the concentration of the feed gas increases from 0.75 to 0.95 mole fraction. As the flow rate of the water increases from 15 to 25 L/min, the concentration of oxygen decreases from 56.2 to 38.6 ppm with a constant membrane area of 3.11 m2.