Biomass dynamics models are the commonly used methods in fishery stock assessment, because of simple model structure and light need of data. This type of models has been used in tuna stock assessments in the Atlantic and Indian Oceans. However, the potential impacts of the shape of surplus production model and fitting criteria were not often investigated in these applications. In this study, we assessed the Indian Ocean albacore (Thunnus alalunga) using ASPIC (A Surplus Production Model Incorporating Covariates), a typical biomass dynamics model using catch and abundance index as the main data. We focused on comparing the results of selecting different surplus production models (FOX and LOGISTIC) and model fitting criteria (Least Sum of Squared Errors or SSE and Least Sum of Absolute Errors or LAV). The results showed that the selection of surplus production models and model fitting criteria obviously impacted the estimates of biological reference points (MSY, F_MSY, and B_MSY). Overall, the former influenced more greatly than the latter. However, the results did not show much difference in the determination of stock status in terms of overfishing or overfished. This study highlights the importance of serious consideration of surplus production model shape and fitting criteria in the applications with biomass dynamics models, based on the fishery and biological characteristics of stock.