Polyurethane cement (PUC) is now commonly used in the reinforcement of old bridges, which exhibit various issues such as poor toughness, temperature-sensitive mechanical properties, and brittle failure. These problems can lead to the failure of the reinforcement effect of the PUC on old bridges in certain operating environments, leading to the collapse of such reinforced bridges. In order to alleviate these shortcomings, in this study, the toughness of PUC is improved by adding polyvinyl alcohol (PVA) fiber, carbon fiber, and steel fiber. In addition, we study the change law of the flexural strength of PUC between −40 °C and +40 °C. The control parameters evaluated are fiber type, fiber volume ratio, and temperature. A series of flexural tests and scanning electron microscope (SEM) test results show that the flexural strength first increases and then decreases with the increase in the volume-doping ratio of the three fibers. The optimum volume-mixing ratios of polyvinyl alcohol (PVA) fiber, carbon fiber, and steel fiber are 0.3%, 0.04% and 1%, respectively. Excessive addition of fiber will affect the operability and will adversely affect the mechanical properties. The flexural strength of both fiber-reinforced and control samples decreases with increasing temperature. Using the flexural test results, a two-factor (fiber content, temperature) BP neural network flexural strength prediction model is established. It is verified that the model is effective and accurate, and the experimental value and the predicted value are in good agreement.