The existence of a global attractor for the following \(p\)-Laplacian equation: \[ u_t-\text{div}\bigl(|\nabla u|^{p-2}\nabla u\bigr)+f(u)=g \quad\text{in } \Omega\times\mathbb{R}^+,\tag{1} \] with the Dirichlet boundary condition \[ u |_{\partial\Omega}=0\tag{2} \] and initial condition \[ u(x,0)=u_0(x)\tag{3} \] is proved in \(W_0^{1,p}(\Omega)\) and \(L^q(\Omega)\) for \(p\geq 2\) and \(q\geq 2\) \((q\) depends on \(f)\). There \(\Omega\subset\mathbb{R}^n\) \((n\geq 3)\) is a bounded domain with smooth boundary \(\partial\Omega\), and the nonlinear term \(f\) is supposed to satisfy the polynomial growth condition of arbitrary order \[ c_1 |u|^q-k\leq f(u)u\leq c_2|u|^q+k,\quad q\geq 2, \] and \(f'(u)\geq-l\) for some \(l\geq 0\), and \(g\in L^s(\Omega)\), where \(s\) satisfies \[ s\geq\min \left\{2,\frac{n(q+p-2)} {p(n+q-1)-n}\right\}. \] The main result states: Under above assumptions the semigroup \(\{S(t)\}_{t\geq 0}\) generated by (1)--(3) with initial data \(u_0\in L^2(\Omega)\) has a \((L^2 (\Omega)\), \(W_0^{1,p}(\Omega)\cap L^q(\Omega))\)-global attractor \({\mathcal A}\), that is \({\mathcal A}\) is compact, invariant in \(W_0^{1,p} (\Omega)\cap L^q(\Omega)\) and attracts every bounded subset of \(L^2 (\Omega)\) in the topology of \(W_0^{1,p}(\Omega)\cap L^q (\Omega)\).