How to image scenes or detect objects hidden from view has been of increasing interest in recent years. Previous studies have demonstrated non-line-of-sight object reconstruction by using time-resolved detectors and a back-projection algorithm, whereas the filtered back-projection method reconstructs high-frequency spatial information, such as the edge of an object, with poor quality. Here we propose an optimized back-projection algorithm to improve the object edge reconstruction quality. We base our method on the observation that the spatial frequency and geometric information required to reconstruct an edge is distributed unevenly across scanning positions of the relay wall. Our method extracts edge voxels from the first projection result, correcting the signal response weight at different scanning positions according to their relative contributions to the object edge reconstruction, and then re-projects data. Simulations and experiments show that compared to the filtered back-projection algorithm, our method achieves better reconstruction results for the object edge, which makes it easier to distinguish the object shape.