In order to explore the widespread applications of Odd Log-Logistic Generalized Gompertz (OLLGG) distribution in fields such as biology, sociology, computer science and marketing, this paper studies a multi-parameter regression model for OLLGG distribution under left-truncated and right-censored data, and estimates the parameters using maximum likelihood thinking. Through numerical simulation, the effectiveness of the estimation method is verified, and the Akaike information criterion is used to select the appropriate distribution form. Finally, the regression model proposed in this article is applied to the channing house dataset to demonstrate its good fitting performance.