We present the radial velocity acceleration of the 6.7 GHz methanol maser in a high-mass star-forming region Monoceros R2 (Mon R2). The methanol maser is associated with an infrared source IRS3. The methanol maser of Mon R2 shows at least three spectral features having radial velocities (Vlsr) of 10.8, 12.7, and 13.2 km s−1. The radial velocity of a feature at Vlsr = 12.7 km s−1 has changed during ten years from Aug. 1999 to Oct. 2009, corresponding to an acceleration of 0.08 km s−1 yr−1. We observed the 6.7 GHz methanol masers of Mon R2 in Oct. 2008 using the Japanese VLBI Network (JVN). Compared with the previous VLBI image obtained in Nov. 1998 using the European VLBI Network (EVN), the maser feature at Vlsr = 12.7 km s−1 showed relative proper motions of ~2.5 mas yr−1 (about 10 km s−1 at 0.83 kpc) toward the intensity peak of IRS3. The radial velocity acceleration could be caused by an inflow from a disk or envelope around a high-mass young stellar object (YSO) at IRS3.