We study the evolution of the luminosity function of a globular cluster system in our Galaxy which is caused by the disruption of clusters, to see how the shape of the observed luminosity function is formed. We examine various disruption processes of clusters, and follow the evolution of clusters in order to reproduce the observed luminosity function as the surviving remnant of the initial cluster system. The present luminosity function can be reproduced if the initial mass function phi is approximated by the power law phi=dN/dM~M^-alpha, with a slope of alpha~2. The luminous side of the luminosity function reflects the initial condition, while the faint side of the luminosity function has been formed by the evaporation process. The absence of old diffuse clusters at present suggests that no such clusters were formed. These results are consistent with the hypothesis that young populous clusters are young globular clusters; the globular clusters of our Galaxy at their formation epoch have the same properties as those of young populous clusters, as observed in the Large Magellanic Cloud (LMC) and other galaxies. We also discuss some applications of our results to globular cluster systems in other galaxies.