We have carried out extensive ^13^CO(J=1-0) observations toward 23 southern H II regions associated with bright-rimmed clouds. In total, 95 molecular clouds have been identified to be associated with the H II regions. Among the 95, 57 clouds are found to be associated with 204 IRAS point sources which are candidates for young stellar objects. There is a significant increase of star-formation efficiency on the side facing to the H II regions; the luminosity-to-mass ratio, defined as the ratio of the stellar luminosity to the molecular cloud mass, is higher by an order of magnitude on the near side of the H II regions than that on the. far side. This indicates that molecular gas facing to the H II regions is more actively forming massive stars whose luminosity is ~>10^3^L_{sun}_. In addition, the number density of the IRAS point sources increases by a factor of 2 on the near side of the H II regions compared with on the far side. These results strongly suggest that the active formation of massive stars on the near side of the H II regions is due to the effects of the H II regions, such as the compression of molecular material by the ionization/shock fronts. For the whole Galaxy, we estimate that the present star-formation rate under such effects is at least 0.2-0.4M_{sun}_/yr, corresponding to a few 10% by mass.