In order to explore the strengthening effect of reinforced concrete beams strengthened by carbon fiber reinforced polymer reinforced geopolymer matrix (FRGM), the mechanical properties of reinforced concrete beams reinforced with flexural reinforcement reinforced concrete in FRGM system were studied by numerical simulation. Three-dimensional finite element models were established to simulate the failure mode, characteristic load and load-mid-span deflection curve of reinforced concrete beams reinforced by FRGM system, and the influence of the thickness and length of the FRGM layer and the pre-damage degree of the original specimen on the reinforcement effect was discussed. The results show that the thickness of the FRGM layer has no obvious effect on the ultimate bearing capacity of reinforced concrete beam, and the increase range is 72.29% ~ 79.38%, but the stiffness of the FRGM layer is improved to a certain extent, up to 38%. The ultimate bearing capacity of reinforced concrete beams can be increased by increasing the length of the FRGM layer, but with the increase of the length of the FRGM layer, the increase of the ultimate bearing capacity gradually weakens, indicating that there is no linear increase relationship between the length of the FRGM layer and the ultimate bearing capacity. Compared with the original components, the bearing capacity of reinforced concrete beam members is improved to a certain extent after pre-damage reinforcement(36.5% ~ 73.66%), which shows the effectiveness of FRGM reinforcement method.