The scouring and deposition of sediment caused by unsteady flows (e.g., storm waves and floods) produces many secondary disasters. The resultant bed-load movement exhibits different transport laws compared with that by steady flow. In this study, the flume experiments were performed to study the bed-load movement under unsteady flow with different velocity skewness. The movement of uniform and non-uniform non-cohesive sediment under unsteady flow as well as the influence of the steady and unsteady flow on sediment transport rate are compared. Additionally, the non-uniform sediment transport formula of fine-to-coarse particle diameter ratio was investigated. The results showed that the sediment transport rate between uniform and non-uniform sand under the same median diameter is different. The non-uniform sediment transport rate is 1.27-, 3.19-, and 0.68-times as large as that in uniform sediment under d₅₀ = 0.664, 1.333, and 2.639 mm under unsteady flow, respectively. For non-uniform sand, the transport rate of non-uniform sand with a larger adjacent particle size ratio (δ = 0.29) was 1.31-times greater than that of the non-uniform sand with a smaller adjacent particle size ratio (δ = 0.50). Moreover, theoretical deduction was carried out and the incipient sediment motion was analyzed from the force mechanism. A new unsteadiness parameter based on the acceleration concept was proposed. The relationship between the travel distance and velocity skewness of sediment particles was set up. The experimental results and theoretical analysis showed that sediment under unsteady flow were easier to start and transport than those under steady flow in the same flow effect. The travel distance of sediment particles was longer under unsteady flow than that under steady flow.