According to the copper-based powder metallurgy friction material with the high stable friction coefficient and the preparation method, the components and the preparation process of the material are optimized, the system matching effect of a copper alloy matrix, a lubricating component and a solid component is exerted, and the obtained copper-based powder metallurgy friction material has the advantages of being high in strength, low in expansion rate, small in deformation amount and good in abrasion resistance; the fluctuation range of the friction coefficient of the friction material does not exceed +/-5%, the average friction coefficient mu cp is larger than or equal to 0.31 and smaller than or equal to 0.34, the fluctuation range of the friction coefficient does not exceed +/-5% of the average friction coefficient, and the linear abrasion loss of the friction material is smaller than or equal to 0.0038 mm/face per time. The obtained friction material has good mechanical strength, is suitable for the working conditions that the positive pressure is 2.032 KN and the speed is 75 m/s, has the advantages of being high in strength, low in expansion rate, small in deformation amount, good in abrasion resistance and the like, does not have the phenomena of friction layer falling, chipping, clamping stagnation, bonding and the like in the using process, and is stable in braking curve and stable and reliable in braking process.