Concentration measurement of oxygen gas is required for better monitoring and control of various types of combustion systems. As compared with conventional zirconia oxygen sensors, tunable diode laser absorption spectroscopy can provide faster response, with smaller interference of inflammable gases. In this paper we report the concentration measurement of oxygen molecules using the absorption band (A-band) of 760 nm wavelength. A periodically poled LiNbO3 crystal (PPLN) is employed for the frequency doubling of 1520 nm light from a distributed feedback laser, resulting in the 760 nm output power of 1.8 mW. The wavelength modulation spectroscopy with dual beam configuration enables the cancellation of the common mode noise from diode laser as well as excess etalon noise that arises from optical paths including the PPLN module. With the cell length of 200 mm, the absorption measurement using the R11Q12 line at 760.445 nm has led to a minimum detectable absorbance of 3.7×10-4 m-1. A dynamic response faster than 1 s was seen when the oxygen concentration was changed between 0% and 24% while the laser wavelength was fixed at the absorption peak.