Abstract: Taking 3-order single-mode laser Lorenz system and 2-order Duffing system as examples,reduced-order hybrid function projective synchronization(RHFPS) between them is studied.By taking different time-varying functions as scaling factors and designing nonlinear controller,the state variables of 2-order Duffing system can track the state variables' variation of the 2-order projective subsystem constructed by the first two state equations of the 3-order single-mode laser Lorenz system according to the given time-varying scaling factors.It is proved that the synchronization error system at the origin is exponentially stable when the gain intensity of nonlinear controller is greater than zero.Simulation experiments show that the proposed RHFPS scheme is feasible and effective,and is robust in a certain degree under the disturbance of white Gaussian noise.