  In this paper, we will count the number of cusps of complete Riemannian
manifolds $M$ with finite volume. When $M$ is a complete smooth metric measure
spaces, we show that the number of cusps in bounded by the volume $V$ of $M$ if
some geometric conditions hold true. Moreover, we use the nonlinear theory of
the $p$-Laplacian to give a upper bound of the number of cusps on complete
Riemannian manifolds. The main ingredients in our proof are a decay estimate of
volume of cusps and volume comparison theorems.
