Abstract: Controlled synchronizibility of non-diffusively coupled complex networks is studied. After the analysis of eigenvalues distribution of outer coupling matrix of non-diffusively coupled complex networks, control law for synchronize non-diffusively coupled complex networks is given. It is found that the smaller the distance between largest and smallest eigenvalues of outer coupling matrix, the stronger the controlled synchronizibility of non-diffusively coupled complex networks. It is also found that the smaller the coupling strength, the greater the possibility that the network can achieve controlled synchronization. However under certain condition a smaller coupling strength requires a larger control gain value. Finally a small-world network formed by coupled Lorenz oscillators which needs to be controlled to synchronize onto chaotic orbit is given as an example to illustrate the effectiveness of the results.