Heteroepitaxial n-Hg0.78Cd0.22Te films with near-surface graded-gap layers were grown by molecular beam epitaxy and subjected to two-stage thermal annealing in saturated mercury vapor atmosphere. The first stage of annealing was carried out for 2 h at a temperature of 360°C. The second stage was carried out at a temperature of 220°C for 24 h. Similar annealing was carried out after As+ ion implantation to activate the introduced impurity and anneal radiation defects. Based on as-grown and annealed films, metal–insulator–semiconductor (MIS) structures were formed by depositing an Al2O3 dielectric by plasma atomic layer deposition. The admittance of fabricated MIS structures was studied in a wide range of frequencies and temperatures. It was found that after thermal annealing, the properties of the n-HgCdTe surface layer are noticeably changed, which is manifested as a decrease in the density of slow states in the transition layer between the dielectric and the semiconductor, and an increase in the generation of minority charge carriers in the n-HgCdTe near-surface layer. These changes in the properties of n-HgCdTe after thermal annealing are associated with the modification of the defect system of the near-surface layer of the semiconductor and the transition layer between dielectric and semiconductor. No significant changes were detected in the bulk properties of the epitaxial film after thermal annealing. A decrease in the density of states near the interface between HgCdTe and Al2O3 during thermal annealing makes it possible to facilitate the electrical characterization of MIS structures by suppressing hysteresis phenomena.