  In this paper, using pseudo-holomorphic curve method, one proves the
Weinstein conjecture in the product $P_1\times P_2$ of two strongly
geometrically bounded symplectic manifolds under some conditions with $P_1$. In
particular, if $N$ is a closed manifold or a noncompact manifold of finite
topological type, our result implies that the Weinstein conjecture in
$\mathbb{C}\mathbb{P}^2\times T^*N$ holds.
