The near-infrared photometric properties of red giant branch (RGB) and horizontal branch (HB) stars in the [Fe/H] approximately -0.3 globular cluster NGC 6553 are investigated using J and H images obtained with the CFHT facility infrared camera. The near-infrared color-magnitude diagram (CMD) of NGC 6553 differs from its optical counterparts in two respects. First, the (H,J-H) diagram does not hook downwards or flatten near the RGB tip. After correcting for differences in distance and reddening, the locus of the NGC 6553 RGB in the (H,J-H) diagram falls redward of the [Fe/H] approximately -0.7 cluster 47 Tuc, and a comparison with isochrones suggests that [Fe/H] greater-than-or-equal-to -0.4, consistent with other metallicity estimates. Second, the NGC 6553 HB is very flat in H, which is different from what is seen at optical wavelengths, where the HB is noticeably tilted. The ratio of supra-HB to zero-age HB stars is similar to what is seen in other metal-rich clusters, but is larger than predicted by evolutionary models.