As an agricultural waste, a large amount of corn stalk will cause environmental pollution. In order to realize the resource utilization of waste and meet the strict requirements of modern traffic on pavement strength and durability, it was modified and applied to an AC-13 asphalt mixture to study its influence on the road performance of asphalt mixture and its mechanism. The road performances of modified corn stalk fiber, lignin fiber, and ordinary asphalt mixtures were evaluated via the wheel tracking test, low-temperature bending test, water immersion Marshall test, freeze–thaw splitting test, and fatigue test. Based on the results of three-point bending fatigue test, the viscoelastic parameters and indexes of the fiber asphalt mixture were obtained by fitting the loading specimen and deflection data with the Burgers constitutive model, and the creep strain response was analyzed by applying dynamic load, so as to explore the relationship between the viscoelastic characteristics and creep behavior of modified corn stalk fiber and AC-13 mixture. The long-term high-temperature performance test of the asphalt mixture with the best fiber content was carried out by using the long-term pavement intelligent monitoring equipment independently developed by the group of investigators. According to the findings, the ideal fiber contents for modified corn and lignin in asphalt mixture are 0.2% and 0.3%, respectively. Among them, the modified corn stalk fiber with a 0.2% content has the best effect on road performance, viscoelastic performance, and the asphalt mixture’s creep behavior under dynamic load. Compared with the 0.3% lignin fiber asphalt mixture, its dynamic stability, bending stiffness modulus, immersion residual stability, freeze–thaw splitting strength ratio, and loading times at failure increased by 19.9%, 18.28%, 4.19%, 8.6%, and 9.15%, respectively. Compared with ordinary asphalt mixture, it increased by 47.0%, 28.72%, 7.65%, 15%, and 75.81%, respectively. Moreover, when modified corn stalk fiber is added at 0.2%, the viscoelastic delay time of asphalt mixture is the longest, the strain peak value and rut depth are at a minimum, and the viscoelastic properties, creep properties, and long-term high-temperature properties are the best.