The generation of betatron radiations by laser-accelerated electron beams is of great interest in the scientific community as it has many applications. In this paper, we propose a new method for the generation of short wavelength betatron radiations. In the new scheme, a high power laser pulse is sent into a capillary plasma waveguide at an off-axis position to intentionally enhance the betatron oscillation amplitude, which can lead to the production of shorter wavelength radiations. We demonstrated that the idea works by 2D particle-in-cell simulations and we also developed a theory to explain the phenomena. In this paper, details of the results are described.