In this paper, we investigate a new kind of the so-called Lognormal-Pareto composite model (LPC), for modeling Algerian cars claims data, where right random censoring sinister payments are considered. The LPC model allows more flexibility over the thickness of the tail. We study the adequacy of the LPC model, using a Monte-Carlo procedure first, and thereafter propose a basic application to car premium relating to a real dataset of Algerian cars claims.