  In this paper, we investigate a class of domains $\Omega^{n+1}_\gamma
=\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^\gamma < |w| < 1\}$ for
$\gamma>0$ that generalizes the Hartogs triangle. We obtain a sharp range of
$p$ for the boundedness of the Bergman projection on the domain considered
here. It generalizes the results by Edholm and McNeal \cite{LD1} for n = 1 to
any dimension n.
