A modified function projective synchronization scheme, multivariable function projective synchronization, is proposed. Different from existing function projective synchronization schemes whose scaling factor is unary function, the scaling factor discussed in this scheme is multivariable function. It implies that synchronization behavior of the proposed scheme is more complicated and more unpredictable. The driver and responding system show correlation in a higher dimension. With modified active control method, controller of the synchronization is designed. In numerical simulations, four-dimensional energy resources system and a new hyperchaotic Chua system are investigated. Multivariable function projective synchronization with two types of scaling factor between two systems are achieved. Based on the synchronization, a secure communication scheme is designed. A secure communication simulation is carried out with sinusoidal signal and gray image signal as information signals. Meanwhile, anti-noise simulation is performed with a wavelet threshold denoising algorithm. It shows that the synchronization method is feasible, and the secure communication scheme is effective.