The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $alpha$ is a spaceform.