  This article is devoted to study the class of backward stochastic
differential equation with delayed generator. We suppose the terminal value and
the generator to be $L^{p}$-integrable with $p>1$. We derive a new type of
estimation related to this BSDE. Next, we establish the existence and
uniqueness result in two ways. First, an approximation technics used by Briand
et al. (Stochastic Process. Appl. 108 (2003) 109-129) and hence the well-know
Picard iterative procedure. Using Picard iterative procedure, we revisit the
result of Dos Reis et al. (Stochastic Process. Appl. 121 (9) (2011) 2114-2150),
simplifying the proof and give an explicit existence and uniqueness condition
related to the Lipschitz constant $K$ and the terminal time $T$.
