The addition of various oils to meat analog has been an important topic to improving its juiciness and tenderness. However, this causes a concern about oil leaching from the meat analog during long-term storage. Here, we aimed to assess the storage stability of vegetable-oil-supplemented meat analogs and analyze the effects of temperature and storage period on their physiochemical characteristics. The meat analogs were prepared by adding 30 g castor oil, orange oil, palm oil, shortening, or margarine vegetable oil based on 100 g of textured vegetable protein. They were then stored at −18 or −60 °C for 6 months and analyzed at one-month intervals. The meat analog supplemented with orange oil had the highest water content (64.85%; 66.07%), hardness (35.48 N; 34.05 N), and DPPH-radical-scavenging activity (30.01%; 30.87%) under −18 and −60 °C, respectively, as well as the highest liquid-holding capacity in different conditions. During frozen storage, temperature barely affected the meat quality. The storage stability of all meat analog samples was maintained for 6 months, although the quality was slightly reduced with an increase in storage duration. Coliform group bacteria were not detected regardless of the storage condition. In conclusion, all results supposed that orange oil can be a promising candidate for improving the juiciness and tenderness of meat analogs, and the quality of samples was maintained for at least 6 months under frozen storage. The findings of this study are relevant to the development and promotion of meat analog as an alternative to animal meat.