The assembled hollow-core slab bridge is the most widely used beam bridge in China. With the increasing traffic volume and traffic load in China, the joints of the hollow-core slab bridge are prone to damage. In this paper, a hollow-core slab bridge with locally curved prestressed tendons is proposed. Based on the static load test of a beam with joints taken from the cross section of a hollow-core slab bridge in practical engineering, a finite element nonlinear analysis is used to simulate the test, and the concrete and interface parameters under the correct analysis results are obtained. Finally, the parameters are applied to the three-beam and two-joint hollow-core slab bridge with a span of 10 m and a finite element analysis is carried out to explore the total failure process and performance improvement effect of the prestressed hollow-core slab bridge. The results show that the interface unit method can successfully simulate the new-to-old concrete interface where the joint is in contact with the precast beam segment. Compared with the static load test results, the analysis error of each finite element model is basically within 15%. Compared with the traditional hollow-core slab bridge, the cracking load, through-joint load, and ultimate load of the prestressed hollow-core slab bridge are increased by 50.0%, 91.7%, and 66.7%, respectively. Under the same load, the stress of the U-bar, the relative deflection of both sides of the joint, and the maximum width of the joint of the prestressed hollow-core slab bridge are lower than those of the traditional hollow-core slab bridge. When the ultimate load is reached, the longitudinal crack lengths of the traditional hollow-core slab bridge and the prestressed hollow-core slab bridge are 0.48 L and 0.4 L, respectively, and the damage degree of the prestressed hollow-core slab bridge is lower than that of the traditional hollow-core slab bridge.