<p>We study the quasi-geostrophic limit of the Boussinesq equations in a periodic channel domain, where the velocity field satisfies the Navier-slip boundary conditions and the density deviation satisfies the homogeneous Neumann boundary condition. By using the generalized potential vorticity to eliminate the pressure term and performing energy estimate, we overcome the difficulties caused by the simultaneous occurrence of fast oscillation and boundary layer. As a consequence, the uniform existence of the solutions with both balanced and unbalanced initial data is obtained. Moreover, the convergence of the solutions with balanced initial data was established by elliptic theory and compactness argument.</p>