The blue shark, Prionace glauca, is the main by-catch species in tuna longline fishery. As one of top species in the oceanic food webs, the blue shark plays an important role in the marine ecosystem. Traditional stock assessment methods are difficult to accurately evaluate the population dynamic for this shark because of limited data. Based on life-history parameters of the blue shark in the North Atlantic, demographic analysis was employed to estimate the demographic parameters and evaluate the potential exploitation for the blue shark. Moreover, we discussed the relationship between age at first capture and critical value of fishing mortality corresponding to the value of intrinsic rate of natural increase 0. The results showed that the survival rate (S) of blue shark from 0.719 to 0.820, intrinsic rate of natural increase (r0) from 0.250 to 0.381, time of population doubling (tx2) from 1.819 to 2.773 years, reproduction rate per generation (R0) from 6.600 to 22.255, and generation time (G) from 8.498 to 10.162 years. The sensitivity analysis for the life history parameters revealed that the uncertainties of natural mortality existed in the first age class, age at maturity and maximum age had slight influence on the demographic parameters. Fishing mortality (Fc) increased with the age at first capture. When the age at first capture (tc) was more than five, there was no obvious relationship between Fc and tc.