External prestressing is widely employed in structural strengthening engineering due to its numerous advantages. However, external prestressed steel bars are prone to corrosion when exposed to the service environment. This paper is dedicated to examining the use of fiber-reinforced polymer (FRP) bars as external prestressing materials to strengthen one-way concrete slabs. Five one-way concrete slabs were strengthened with externally prestressed FRP bars with different prestress levels and different amounts of FRP bars, while one non-strengthened slab was used for comparison. The effects of strengthening on the flexural behavior, specifically the cracking load, ultimate load, stiffness and failure mode, were analyzed systematically. Moreover, the ductility and cost–benefit optimizing properties of the reinforcing design were discussed. The results show that external prestressed FRP bars significantly improve the cracking load, ultimate load and stiffness of one-way concrete slabs. The absence of a bond between the concrete and FRP bars overcomes the brittleness of the FRP bars, while the strengthened slabs exhibit satisfactory ductility and a higher post-yield stiffness and bearing capacity. Additionally, the cost/benefit ratio is optimized by increasing the prestress level, while a higher number of prestressed FRP bars is beneficial to ductility. Finally, a method for calculating the stress in prestressed FRP bars at ultimate loads was proposed. Irrespective of the prestressing material, this method is applicable to both strengthened beams and one-way slabs.