Abstract: In this thesis the evolution models and the pulsating property of 15M ⊙, 20M ⊙and 30M ⊙stars are calculated under different metallicities in order to understand the dependence of the period-luminosity relation on the metallicity.The opacities up-to-date, overshooting from the convective core and mass loss through the stellar wind are included in our evolution models. In order to get better consistence with the observed blue-to-red ratio of supergiant numbers,the ratio of the mixing-length to local pressure scale height of 1.0 and 1.8 in the convection zone is adopted.It is found that normal models without overshooting seems to produce too many blue supergiants while overshooting models seems to produce too many red supergiants, but neither of them can correctly predict the tendency of increasing the B/R ratios with increasing the metal abundance observed in many stellar systems. This result seems to indicate that the overshooting from the convective core is strong in extremely metal-poor stars and fades gradually away with the increase of the metal abundance. With a proper combination of model parameters we have constructed a series of stellar models with α=1.0 that give theoretical B/R ratios in better consistence with the observations, and these models have been used to calculate the period-luminosity relation for the RSG long-period variables. The theoretical P-L relations for observed long-period variables in the LMC, M33 and our Milky Way are compared. The observed LPVs are in good agreement with the P-L relations of the fundamental mode for the LMC and M33, but the LPVs in the MW seems to have shorter periods and more likely to be the first overtone pulsators. We have found that the period-luminosity relations under different metallicities show a tendency of decreasing the luminosity and increasing the period with the increase of the metal abundance, and the correction of the luminosity at a given period is δM _bol～0.83δlgZ.