The rotor system is an important part of large-scale rotating machinery. Bearings, as a key component of the rotor system, play a vital role in the healthy operation of the rotor system. The bearings operate under harsh conditions such as high temperature, high pressure, and high speed. They are complex and extremely prone to failure, especially when the bearing is affected by impact load, which seriously affects the remaining service life of the bearing. Uneven bearing friction, caused by the impact, is one of the main factors that cause premature failure of the bearing. The early identification of shock loads and reasonable measures are extremely important for the safe operation of equipment. This paper proposes an impact load identification method based on the sparse decomposition of the Mini-max concave penalty function (Mini-max concave penalty function, MC). The method uses the MC penalty function to reconstruct the regularized sparse recognition model, and then uses the improved original dual interior point method to solve the problem. This model realizes the identification of vibration and shock loads. Relevant experimental verification was carried out, and the results show that the sparse decomposition result based on the MC penalty function is better than the L1-regularized sparse decomposition result, and the noise is well suppressed in the non-loaded area of the impact load. This method can be applied to the early fault diagnosis of the vibration signal of the gas turbine rotor.