  In this paper, we consider the finite time blow up of solutions for the
following two kinds of nonlinear wave equations on de Sitter spacetime
\begin{eqnarray*} &&\square_g=F(u),\\ &&\square_g=F(\partial_tu,\nabla u).
\end{eqnarray*} This proof is based on a new blow up criterion, which
generalize the blow up criterion in Sideris \cite{Sider}. Furthermore, we give
the lifespan estimate of solutions for the problems.
