In recent years, near-surface-mounted (NSM) FRP technology has increasingly been used to reinforce historic timber structures. It is valued for its durability, effective reinforcement, and preservation of the building’s appearance. While circular-section beams are commonly found in timber structures, research on their reinforcement with NSM FRP remains limited. To address this gap, this paper establishes a 3D finite element model to investigate the bending performance of circular timber beams reinforced with NSM FRP plates. The model accounts for the orthogonal anisotropic elastoplastic behavior of wood and the progressive elasticity of FRP plates. The validity of the model is confirmed against experimental data. Further parametric analysis explores the impact of FRP reinforcement ratio, FRP reinforcement configuration, modulus of elasticity ratio, and groove size on the bending strengthening efficiency. The results indicate that the optimal FRP reinforcement solution featuring a single-bottom groove configuration with a 1.2% reinforcement ratio and 22.6 modulus ratio achieves the best comprehensive performance for circular timber beams (50.7% load capacity increase, 31.8% initial stiffness improvement, and 23.4% displacement enhancement). A 12 mm groove width avoids both over- and under-reinforcement issues. This approach considers both material cost and strengthening effectiveness while maximally preserving the original appearance of historic structures. The research results can provide a reference basis for the engineering application of NSM FRP plates reinforced circular timber beams.