In this paper we study the dynamic bifurcation of the Swift-Hohenberg equation on a periodic cell ${Omega}=[-L,L]$. It is shown that the equations bifurcates from the trivial solution to an attractor $mathcal{A}_{lambda}$ when th control parameter ${lambda}$ crosses the critical value. In the odd periodic case $mathcal{A}_{lambda}$ is homeomorphic to $S^1$ and consists of eight singular points and thei connecting orbits. In the periodic case, $mathcal{A}_{lambda}$ is homeomorphic to $S^1$, an contains a torus and two circles which consist of singular points.