In order to reduce the radiation dose of X-rays, we present a total generalized variation constrained weighted least-squares approach for low-dose computed tomography (CT) reconstruction. Incorporating the total generalized variation regularization, a total generalized variation constrained weighted least-squares (TGV-WLS) approach is presented to reduce the noise in the projection (sinogram) domain, and the image is then reconstructed using the conventional filtered back-projection (FBP) algorithm. The root mean square errors (RMSEs) of the Shepp-Logan image reconstructed by the TGV-WLS method are reduced by 25.06%, 1.497%, and 15.21%, and the signal-to-noise ratio (SNR) values increased by 10.29%, 0.53%, and 5.68%, respectively, as compared with those of the Gibbs constrained weighted least-squares (Gibbs-WLS), dictionary learning constrained weighted least-squares (DL-WLS), and total variation constrained weighted least-squares (TV-WLS) methods. In addition, for the Clock images reconstructed by the TGV-WLS method, the RMSEs are reduced by 42.72%, 23.45%, and 34.63%, and SNR values increased by 27.04%, 11.42%, and 15.49%, respectively, as compared with those of the Gibbs-, DL-, and TV-WLS methods. The experimental results show that the TGV-WLS method can achieve noticeable gains in terms of noise-induced artifact suppression and edge information and structural details preservation.