Recent narrow-band Ca photometry discovered two distinct red giant branch (RGB) populations in some massive globular clusters (GCs) including M22, NGC 1851, and NGC 288. In order to investigate the dierences in light/heavy elements abundances between the two subpopulations, we have performed low-resolution spectroscopy for stars on the two RGBs in these GCs. We find a significant difference (more than 4) in calcium abundance from the spectroscopic HK0 index for both M22 and NGC 1851. We also find a more than 8 difference in CN band strength between the Ca-strong and Ca-weak subpopulations. For NGC 288, however, we detect the presence of a large difference only in the CN strength. The calcium abundances of the two subpopulations in this GC are identical within errors. We also find interesting differences in CN-CH relations among these GCs. While CN and CH indices are correlated in M22, they show an anti-correlation in NGC 288. However, NGC 1851 shows no dierence in CH between two groups of stars having different CN strengths. The CN bimodality in these GCs could be explained by pollution from intermediate-mass asymptotic giant branch stars and/or fast-rotating massive stars. For the presence or absence of calcium bimodality and the differences in CN-CH relations, we suggest these would be best explained by how strongly type II supernovae enrichment has contributed to the chemical evolutions of these GCs.