Microfluidic devices with the gas permeability through polymer membranes were developed for further high-efficiency of gas-liquid chemical reactions and high-accuracy of environmental diagnosis. The devices were composed of a cover glass and a polydimethylsiloxane (PDMS) chip which has the ability to permeate various gases, because PDMS is made of the elastomeric material. In the chip, microchannels with a width ranging from a few micrometers to a few hundred micrometers were manufactured by using the cryogenic micro machining. The gas permeation phenomena in microchannels are dominated by several factors, such as the gas and liquid flow rates, the membrane thickness between gas and liquid flow, and the surface area of membranes. The advantage of the present work is to realize the simple control of the gas permeability by changing the surface roughness of PDMS, because the cryogenic micro machining enables to control the surface roughness of microchannels and the increase in its roughness yields that in the surface area of membranes. For the evaluation of the gas permeability, the velocity and dissolved gas concentration distribution in the liquid flow field were measured by utilizing micron-resolution particle image velocimetry combined with laser induced fluorescence, and the measurement system was based on the confocal microscope to improve the depth resolution drastically. The experiments were performed under the several conditions with a change in the gas flow rate, the PDMS membrane thickness and the surface roughness, which affect the gas permeation phenomena. The results indicate that the velocity-vector distributions in the liquid flow have a similar pattern and the magnitudes of the velocity are approximately the same values under all conditions, while the dissolved gas concentration distributions have different patterns. It was quantitatively clear that the gas permeability through PDMS membranes was increased with an increase in the surface roughness and has the linearity to the surface area of membranes. The important conclusion is that the proposed device achieves to control the gas permeability by using the elastomeric material and changing the surface roughness.