In this paper, a new treatment of the dbar method for electrical capacitance tomography with a non-circular sensor is presented. It is a direct algorithm of image reconstruction and the gray value at any pixel of the reconstructed image is obtained directly and independently. The major calculations of image reconstruction in the dbar method were implemented in a circular sensor. As a result, complicated calculations of the scattering transform required by a non-circular sensor were avoided. A unique conformal transformation was used to map a circular sensor onto a non-circular sensor, eg a square sensor. In the experiments, a square sensor was constructed and the reconstructed results validated the feasibility and effectiveness of the dbar method in electrical capacitance tomography with a non-circular sensor.