Costaria costata is a new large economic brown alga with potential. Mastering the suitable conditions for its growth and development and its regulation mechanism is the premise of developing the cultivation industry. At present, reports have focused on the gametophyte stage, and temperature is one of the most critical factors affecting algal growth and development. In this study, we investigated the growth and antioxidant physiological characteristics of young sporophyte of C. costata at 6–22 ℃ in order to explore its temperature-adaptation mechanism and provide a theoretical basis for the cultivation of C. costata in sea areas. At the early stage of culture (within 5 days), the relative growth rate (RGR) of young sporophyte of C. costata was the largest at 18 ℃, and the algae were severely perforated and rotted at 22 ℃; with the extension of culture time (10 days), the RGR of algae was the highest at 10 ℃. There was no significant difference in F_v/F_m at different temperatures. During the experimental period, the total photosynthetic rate (P_t) and net photosynthetic rate (P_nmax) of algae were higher at 6–14 ℃. P_nmax was highest at 10 ℃ at 5–10 d. Respiration rate (R_d) was highest at 6 ℃ at 3 d. Algal R_d increased with culture time at 22 ℃. Enhanced respiration is a common response of the young sporophytes of C. costata to low and high-temperature stresses. At 22 ℃, the pigments Fucox and Car, soluble proteins play an active role. At 6 ℃, SOD is the main antioxidant enzyme that scavenges reactive oxygen species. Temperature positively regulates the accumulation of ash, carbohydrate, and crude fiber in the range of 6–18 ℃. In summary, the young sporophytes of C. costata can grow at 6–18 ℃, of which 10 ℃ is preferable.