Finite time control and finite time function projective synchronization for complex networks are studied in this paper. The complex networks with time-varying delay and function projective synchronization are achieved in finite time. The method of pinning control is used to achieve the finite time projective synchronization. A few target nodes are chosen to finish pinning function projective synchronization in a finite time by construct a time-dependent Lyapunov function. An example is provided to illustrate the correctness of the theoretical analysis.