We report interferometric observations of 2.6 mm CO emission and spectroscopy of 2 micron H_2_ emission at the center of the cD/Seyfert galaxy NGC 1275. The CO emission shows an asymmetric structure which is elongated westward up to 10 kpc from the nucleus. In the central 3 kpc, the CO emission mainly originates from two strong peaks. One of the two peaks is located ~1.2 kpc west of the nucleus, while the other peak is ~1.2 kpc east of the nucleus. These two peaks are connected with an arc- shaped region in the south of the nucleus. The velocity structure of CO emission in the central region suggests a rotation around the nucleus with a radius of 1.2 kpc. In contrast to the CO emission, the distribution of 2 micron H_2_ emission is concentrated at the center and is unresolved with our 2" (r ~ 340 pc) slit. A velocity profile of the H2 emission is resolved with a resolution of 30 km s^-1^ and fitted by a Gaussian curve with FWHM of 250 km s^-1^. Many of the physical properties of the CO and H_2_ emission in r < 1.5 kpc are found to be similar to those in the same region of NGC 1068.