The study of HIV infection, transmission and spread of AIDS is quite common by the use of stochastic model. The estimation of expected time to seroconversion of HIV infected over the time interval (0, t] is an important aspects which help medical intervention. In this paper focuses on the study of a stochastic model for predicting the seroconversion time when the intercontact times form a geometric process using geometric distribution as the threshold. In this study the theoretical results are substantiated by using numerical data simulated.