In this work, CeO2 nanoparticles, as well as CeO2 nanocomposites with plasmonic silver nanoparticles, were synthesized using a simple sol-gel process. The concentration of silver in the composites varied from 0.031–0.25 wt%. Cerium hydroxide dried gel was calcined at temperatures from 125 to 800 °C to obtain CeO2. It was shown that, at an annealing temperature of 650 °C, single-phase CeO2 nanopowders with an average particle size in the range of 10–20 nm can be obtained. The study of acid-base properties showed that with an increase in the calcination temperature from 500 to 650 °C, the concentration of active centers with pKa 9.4 and 6.4 sharply increases. An analysis of the acid-base properties of CeO2-Ag nanocomposites showed that with an increase in the silver concentration, the concentration of centers with pKa 4.1 decreases, and the number of active centers with pKa 7.4 increases. In a model experiment on dye photodegradation, it was shown that the resulting CeO2 and CeO2-Ag nanopowders have photocatalytic activity. CeO2-Ag nanocomposites, regardless of the silver concentration, demonstrated better photocatalytic activity than pure nanosized CeO2.