Based on the Lyapunov stability theory, the Lyapunov function in the form of exponential type is constructed. The four-variable Chen hyperchaotic model is investigated as an example. The reliability of a linear coupling-inudced synchronization of hyperchaotic system is proofed analytically. Furthermore, the modulation effect of nonlinear coupling on the synchronization induced by linear coupling is investigated. A statictical function is defined to evaulate the power consumption of controller according to the dimensionaless dynamical equations, the appropriate parameter region for synchronization due to the joint action of linear and nonlinear coupling, and the extensive numerical results confirm the correctress of the theoretical predication.