This paper focuses on the study of a stochastic model for predicting seroconversion time of HIV transmission under correlated intercontact times. In the estimation of expected time to seroconversion, there is an important role for the interarrival times between successive contacts and it has a significant influence. We propose a stochastic model assuming the intercontact times between successive contacts are correlated random variables and the threshold distribution is SCBZ property. The expected time to seroconversion and its variance are derived and numerical illustrations are provided.