As an imaging technique with low radiation dose and improved contrast, digital x-ray tomosynthesis is widely used in clinical diagnoses. Based on the superior capability of x-ray phase-contrast imaging (PCI) techniques for imaging low density materials, the combination of X-ray tomosynthesis and PCI can potentially provide higher efficiency in the detection of soft tissues. The goal of this work was to develop a fast imaging method for phase-contrast tomosynthesis, called fast grating-based phase-contrast tomosynthesis (GPC-Tomo), which integrates tomosynthesis with a grating-based PCI technique. Following the interlaced phase-stepping (PS) data collection method, which is much faster than conventional PS method, we propose a novel image reconstruction method called inner-focusing (IF) reconstruction for the fast GPC-Tomo. The proposed IF reconstruction method was validated by real experiments and the results suggested its effectiveness in achieving a fast GPC-Tomo.