  We study the asymptotic behavior of nonnegative solutions of the semilinear
parabolic problem
  {u_t=\Delta u + u^{p}, x\in\mathbb{R}^{N}, t>0
  u(0)=u_{0}, x\in\mathbb{R}^{N}, t=0.
  It is known that the nonnegative solution $u(t)$ of this problem blows up in
finite time for $1<p\leq 1+ 2/N$. Moreover, if $p> 1+ 2/N$ and the norm of
$u_{0}$ is small enough, the problem admits global solution. In this work, we
use the entropy method to obtain the decay rate of the global solution $u(t)$.
