A mechanical model of a circular section of a tunnel roadway considering damage is established to improve the impact protection performance of the “roadway rock-support” system and provide a theoretical basis for designing coal mine impact ground pressure roadway support. The formula of the critical rock burst load of a circular roadway is derived according to the instability theory of rock burst disturbance response. The influence of mechanical properties of surrounding rock and roadway support strength on the critical rock burst load of a roadway rock-support system is studied using the control variable method. The research shows that 1) under the support condition of a roadway, with the increase of uniaxial compressive strength, softening modulus, and internal friction angle of surrounding rock, the critical rock burst load of a roadway has an increasing trend; the critical rock burst load of roadway decreases with the increase of the elastic modulus of the surrounding rock. 2) Under the condition of no support, with the increase of uniaxial compressive strength, elastic modulus, and internal friction angle of surrounding rock, the critical rock burst load of roadway tends to increase. With the decrease of the surrounding rock’s softening modulus, the critical rock burst load of the roadway decreases. When the aforementioned four kinds of surrounding rock influence factors are the same, the critical load of rock burst under the supporting condition is much larger than that under the non-supporting condition. 3) A new impact tendency index K is defined as the ratio of the softening modulus and the elastic modulus. 4) The critical load of rock burst increases approximately linearly with the increase of support stress. The critical load of a rock burst is about 400 times as large as the supporting stress. Increasing roadway support strength can greatly improve the stability of the supporting and roadway surrounding rock system, and the stability of the supporting and roadway surrounding rock system can be improved by reasonably changing the mechanical properties of the surrounding rock.