In this work, we report on the development of an advanced multi-channel (MC) image reconstruction algorithm for grating-based X-ray phase-contrast computed tomography (GB-XPCT). The MC reconstruction method we have developed operates by concurrently, rather than independently as is done conventionally, reconstructing tomographic images of the three object properties (absorption, small-angle scattering, refractive index). By jointly estimating the object properties by use of an appropriately defined penalized weighted least squares (PWLS) estimator, the 2nd order statistical properties of the object property sinograms, including correlations between them, can be fully exploited to improve the variance vs. resolution tradeoff of the reconstructed images as compared to existing methods. Channel-independent regularization strategies are proposed. To solve the MC reconstruction problem, we developed an advanced algorithm based on the proximal point algorithm and the augmented Lagrangian method. By use of experimental and computer-simulation data, we demonstrate that by exploiting inter-channel noise correlations, the MC reconstruction method can improve image quality in GB-XPCT.