The function projective synchronization of chaotic system with a new kind of scaling function is proposed in this paper. In general, the scaling function factor of function projective synchronization is a function of the time variable. However, in this paper, the scaling function factor we discussed is a function of state variable which imply that this kind of synchronization is more complicated. Via modified active control method, the controller of the proposed synchronization is designed, and successfully applies to the four dimensional energy resources system and a new hyperchaotic Chua system. Numerical simulation is presented to show the validity of the controller and the proposed synchronization.