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Calderon's method was generalized to electrical capacitance tomography (ECT) for sensors of square cross sections in this paper. It is a direct algorithm of image reconstruction, as neither matrix inversion nor an iterative process is required for image reconstruction. Since the major calculations are implemented in terms of a circular region, complicated calculations required by Calderon's method for a noncircular cross section are avoided. A unique conformal transformation was used to establish a map from a circular region to a square. Results were obtained for a sensor of square cross section by using the conformal transformation. Two approximations of the scattering transform used in Calderon's method were compared with simulated data. The Gauss-Legendre quadrature was applied to provide a fast-speed and high-quality image reconstruction. The reconstructed results validated the feasibility and effectiveness of the proposed treatment of Calderon's method in ECT with a sensor of noncircular cross section.