This paper deals with homogeneous Dirichlet boundary value problem to a
class of semi-linear equations with p-Laplacian viscoelastic term $$
\frac{\partial
u}{\partial t}-\Delta
u+\int_{0}^{t}g(t-s)\Delta_{p}u(x,s)\mbox{d}s=\mid
u\mid^{q(x)-2}u,~~~~~x\in\Omega,~~t\geq
0, $$ the bounded domain $\Omega\subset
R^{N}~(N\geq 1)$ with a smooth
boundary. We prove that the weak solutions of the above problems blow up
in finite time for all $q^{-}>
2k$(~$k$~is defined in $(2.3)$),
when the initial energy is positive and the
function~$g$~satisfies suitable
conditions. This result generalized and improved the result by
S.~A.~Messaoudi~