We considered the Boussinesq maximal estimate when $n\ge 1$. We obtained the Boussinesq maximal operator ${\mathcal{B}}_E^{\ast }f$ is bounded from $L^2({\mathbb{R}}^n)$ to $L^2({\mathbb{R}}^n)$ when $f\in L^2({\mathbb{R}}^n)$ and $\text{supp}\hat{f}\subset B(0,\lambda )$.