In this paper we develop a robust procedure to estimate regression coefficients for a linear model with censored and truncated data based on simplicial regression depth. Simplicial depth of a point is defined as the proportion of data simplices containing it. This simplicial depth can be extended to regression problem with censored and truncated data. Any line can be given a depth and the deepest regression line is the line with the maximum simplicial regression depth. We show how the proposed regression performs through analyzing AIDS incubation data.