Methylosinus trichosporium OB3b is a methanotrophic bacterium containing particulate methane monooxygenase (MMO), which catalyzes the hydroxylation of methane to methanol. The methanol is further oxidized to formaldehyde by methanol dehydrogenase (MDH). We developed a novel compulsory circulation diffusion system for cell cultivation. A methane/air mixture (1:1, v/v) was prepared in a tightly sealed gas reservoir and pumped into a nitrate mineral salt culture medium under optimal conditions (5 ${mu}M$ $CuSO_4$, pH 7.0, $30^{circ}C$). Cells were harvested, washed, and resuspended (0.6 mg dry cells/mL) in a 500 mL flask in 100 mL of 10 mM phosphate buffer (pH 7.0) containing 100 mM NaCl and 1 mM EDTA as MDH inhibitors, and 20 mM sodium formate. A single 12 h batch reaction at $25^{circ}C$ yielded a final concentration of 13.2 mM methanol. The use of a repeated batch mode, in which the accumulated methanol was removed after each of three 8 h cycles over a 24 h period, showed a productivity of 2.17 ${mu}mol$ methanol/h/mg dry cell wt. Finally, a lab-scale reaction performed using a 3 L cylindrical reactor with a working volume of 1 L produced 13.7 mM methanol after 16 h. Our results identify a simple process for improving the productivity of biologically derived methanol and, therefore the utility of methane as an energy source.