Variations in environmental variables and measurement errors often result in large and heterogeneous deviations in fitting fish stock-recruitment (SR) data to an SR statistical model. In this work, the maximum likelihood method was used to fit the seven statistical SR models on seven sets of simulated SR data. The best relationships were selected using AIC (Akaike Information Criterion) and BIC (Bayesian Information Criterion) methods, respectively, which has the advantage of testing the significance of the difference between the functions of different model specifications. The method was also utilized on eight sets of real fisheries SR data. The results showed that both AIC and BIC are valid in selecting the most suitable SR relationship. As far as the nested models are concerned, BIC is better than AIC.