The annual maximum earthquake magnitudes around Taiwan from 1900 to 2009 are presented in this paper. Using the distribution of the AMEM, a probabilistic framework to estimate the recurrence probability of a large-size earthquake is also proposed and an illustration was made in this paper. The mean value of the 110-AMEM is 6.433, and the coefficient of variation is around 10%. The results of two goodness-of-fit tests show that the Gamma and lognormal distributions are relatively suitable to represent the AMEM around Taiwan among five common probability distributions. Using the proposed approach, the recurrence probability is 4% for an earthquake with magnitude greater than 7.5 in a 1-year period around Taiwan. More site-specifically, the probability is around 5% in Central Taiwan for such an earthquake to occur in a 50-year period.