There is relatively little information on the biology of Indian Ocean albacore tuna (Thunnus alalunga); further, many problems with the fishery data result in a large uncertainty in its stock assessment results and affect fishery management. In this study, based on the fishery catch, standardized Catch Per Unit Effort (CPUE) data, and relevant stock hypotheses of Indian Ocean albacore tuna, a Bayesian biomass dynamic model was used to conduct a stock assessment. The results showed that: (1) The observation error of catch has an important influence on the estimation of model parameters, judgment of resource status, and fishery management, and an increase in catch observation error increases the probability of overfishing assessed by the model, which leads to a decrease in Total Allowable Catch (TAC); (2) The shape parameters of biomass dynamic model, prior distribution of r, and choice of resource abundance index affect the quality of stock assessment, and this study shows that the stock assessment results of the Fox model are more reasonable than those of the Schaefer model, the increase in the range of r priori distribution makes the resource state assessed by the model better, and the assessment results are relatively better when using the standardized CPUE of the southwest waters; (3) Setting a range of resource proportions (φ、P₂₀₁₇) for certain years can help improve the quality of fishery stock assessment under the lack data; (4) The probability of overfished and overfishing for albacore tuna in the Indian Ocean are 34% and 50%, respectively, and the probability of both occurring simultaneously is 32%, and the species is at risk of overfishing. The projection analysis showed that the probability of not overfishing for Indian Ocean albacore tuna after 10 years was greater than 60% when the TAC was controlled below 32658 t (i.e., 90% of the final five-year average catch). The Bayesian biomass dynamic model, as a data-limited fishery stock assessment model, is applicable to Indian Ocean albacore tuna, and it can better consider the effects of parameter inputs and uncertainty factors on the quality of stock assessment and the estimation of TAC, providing a scientific basis for an in-depth study of the stock status and management of Indian Ocean albacore tuna.