A fast prediction method for forced vibration response of bladed disks with contact interfaces was established. This method was exemplified by applying it into a finite element (FE) model of a bladed disk with dovetail joints. The linear part of the finite element model was reduced by means of the modal synthesis method. A reduced model with the total amount of the generalized degree-of-freedoms less than 1/25 that of the full model was set up. Forced response was predicted by employing the harmonic balance method. In this process, the Jacobian acceleration technique proposed in previous research effort was reformulated and improved. It evolved into a improved and fast Jacobian-evaluation method suitable for large-scale non-linear bladed disk models with contact interfaces. Result showed that the response prediction based on the harmonic balance method was more than 400 times faster. Prevailing advantages in computational efficiency and accuracy were fully demonstrated by the simulation results. This can raise the potentiality of acting as a powerful tool for the design and optimization for various dry friction dampers.