Real-life networks often encounter vertex dysfunctions, which are usually followed by recoveries after appropriate maintenances. In this paper we present our research on a model of scale-free networks whose vertices are regularly removed and put back. Both the frequency and length of time of the disappearance of each vertex depend on the degree of the vertex, creating a heterogeneous control over the network. Our simulation results show very interesting growth pattern of this kind of networks. We also find that the scale-free property of the degree distribution is maintained in the proposed heterogeneously controlled networks. However, the overall growth rate of the networks in our model can be remarkably reduced if the inactive periods of the vertices are kept long.