In this paper a copula-graphic estimator is proposed for left-truncated and right-censored survival data. It is assumed that there is some dependent censoring acting on the variable of interest, which may come from an existing competing risk. Furthermore, the full process is independently right-censored by some administrative censoring time, while there is an independent left-truncation variable which complicates the sampling procedure. The dependent censoring is modeled through an Archimedean copula function, which is supposed to be known. An asymptotic representation of the estimator as a sum of independent and identically distributed random variables is obtained and, consequently, a central limit theorem is established. These results extend to the truncated setting those in de U˜ña-Álvarez and Veraverbeke(2013). We investigate the finite sample performance of the estimator through simulations. A real data illustration is included.