In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.