Consider the initial value problem of the Ginzburg-Landau wave equation with a general power self-interaction term: \[ (*)\quad \phi_ t=(1+i\alpha)\Delta \phi +(1+i\beta)\phi -(1+i\gamma)| \phi |^{\mu -1}\phi,\quad x\in {\mathbb{R}}^ n,\quad t>0, \] \[ \phi (x,0)=\phi_ 0(x),\quad x\in {\mathbb{R}}^ n, \] where \(\phi\) is a complex scalar function, \(\alpha\),\(\beta\),\(\gamma\in {\mathbb{R}}\), \(\mu\geq 2\), \(i=\sqrt{-1}\), and \(n=1,2,3\). It is shown that for \(\mu \leq 1+4/n\) and any \(\phi_ 0\in H^ 2({\mathbb{R}}^ n)\), Eq. (*) has a unique global solution \(\phi \in C([0,\infty);H^ 2({\mathbb{R}}^ 2))\cap C^ 1([0,\infty);L^ 2({\mathbb{R}}^ n)).\)