We present Heinrich Hertz Telescope CO observations of the shell structure near the active star-forming complex W51A to investigate the process of star formation triggered by the expansion of an H II region. The CO observations confirm that dense molecular material has been collected along the shell detected in Spitzer IRAC images. The CO distribution shows that the shell is blown out toward a lower density region to the northwest. Total hydrogen column density around the shell is high enough to form new stars. We find two CO condensations with the same central velocity of 59 km s^–1 to the east and north along the edge of the IRAC shell. We identify two young stellar objects in early evolutionary stages (Stage 0/I) within the densest molecular condensation. From the CO kinematics, we find that the H II region is currently expanding with a velocity of 3.4 km s^–1, implying that the shell's expansion age is ~1 Myr. This timescale is in good agreement with numerical simulations of the expansion of the H II region (Hosokawa & Inutsuka). We conclude that the star formation on the border of the shell is triggered by the expansion of the H II region.