In this paper, preparation and the inhibition properties of a cationic hyperbranched polymer (HBP-HTC) on clay hydration and swelling were researched. The properties of HBP-HTC, including chemical structure, cationic degree, and molecular weight, were investigated by using Fourier transform infrared (FTIR) spectroscopy, nuclear magnetic hydrogen spectroscopy, sodium tetraphenylborate back titration, and gel permeation chromatography. The obtained results indicated that HBP-HTC was a hyperbranched unsaturated polyester amide with a low molecular weight and high cation degree, with corresponding values of 34,730 and 43.26%, respectively. The inhibition properties of HBP-HTC on clay hydration and swelling were evaluated through linear anti-swelling, water flushing, rolling recovery, and core flooding tests. The results showed that HBP-HTC has an excellent anti-swelling and long-term effect. When 1.0 wt % HBP-HTC was added, the initial anti-swelling rate reached 91.58%. After flushing 10 times with water, the anti-swelling rate remained at 85%. The two cutting rolling recoveries exceed 70%, and the permeability damage rate of HBP-HTC to the core was lower, just 7.03%, which indicated that HBP-HTC effectively inhibited the clay hydration and swelling, had an excellent anti-washing capacity, and also reduced the permeability damage to the core in the process of waterflooding. The inhibiting mechanism of HBP-HTC was revealed by FTIR, zeta potential, X-ray diffraction, X-ray photoelectron spectroscopy, scanning electron microscopy, and contact angles tests. The results exhibited that HBP-HTC neutralized negative charges on the surface of clay to compress the electric double layer. Besides, HBP-HTC was strongly adsorbed on the surface of clay particles due to the highly concentrated cations and hydrogen bonds at the end of the molecule and a large number of hyperbranched molecular chains and formed a waterproof polymer film, preventing water invasion of the clay interlayer, inhibiting clay hydration swelling.