The transport of sediments by a fluid flow is commonly found in nature and in industry. In nature, it is found in rivers, oceans, deserts, and other environments. In industry, it is found in petroleum pipelines conveying grains, in sewer systems, and in dredging lines, for example. This study investigates experimentally the transport of the grains of a granular bed sheared by a turbulent liquid flow. In our experiments, fully developed turbulent water flows were imposed over a flat granular bed of known granulometry. Under the tested conditions, the grains were transported as bed load, i.e., they became entrained by rolling and sliding over each other, forming a moving granular layer. The present experiments were performed close to incipient bed load, a case for which experimental data on grains velocities are scarce. Distinct from previous experiments, an entrance length assured that the water stream over the loose bed was fully developed. At different water flow rates, the moving layer was filmed using a high-speed camera, and the grains' displacements and velocities were determined by post-processing the images with a numerical code developed in the course of this study. The bed-load transport rate was estimated and correlated to the water flow conditions.