High quality J, H and K' images are used to investigate the morphological properties of the near-infrared color-magnitude diagrams for five metal-poor bulge globular clusters and three halo clusters. Photometric parameters to describe the RGB shape, i.e., the colors at fixed magnitudes of M_K=M_H=(-5.5, -5, -4 and -3), the magnitudes at fixed colors of (J-K)o = (J-H)o = 0.70, and the RGB slope, have been measured from the fiducial normal points of the CMDs. We also measured the near-infrared magnitudes of the RGB bump and tip on the luminosity function of the RGB stars for each cluster. The RGB parameters of the observed metal-poor bulge and halo clusters are consistent with the previous empirical relationships between the RGB parameters and the cluster metallicity for metal-rich bulge clusters and halo clusters. The near-infrared magnitudes of the RGB bump and tip are in good agreement with the theoretical prediction of the Yonsei-Yale isochrone.