Given that the computed tomography (CT) reconstruction algorithm based on compressed sensing (CS) results in blurred edges, we propose a modified Canny operator that assists the CS algorithm to accurately capture an object's edge, to preserve and further enhance the contrasts in the reconstructed image, thereby improving image quality. We modified two procedures of the traditional Canny operator, namely non-maximum suppression and edge tracking by hysteresis according to the characteristics of low-dose CT reconstruction, and proposed two major modifications: double-response edge detection and directional edge tracking. The newly modified Canny operator was combined with the CS reconstruction algorithm to become an edge-enhanced CS (EECS). Both a 2D Shepp-Logan phantom and a 3D dental phantom were used to conduct reconstruction testing. Root-mean-square error, peak signal-to-noise ratio, and universal quality index were employed to verify the reconstruction results. Qualitative and quantitative results of EECS reconstruction showed its superiority over conventional CS or CS combined with different edge detection techniques, such as Laplacian, Prewitt, Sobel operators, etc. The experiments verified that the proposed modified Canny operator is able to effectively detect the edge location of an object during low-dose reconstruction, enabling EECS to reconstruct images with better quality than those produced by other algorithms.