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A model of the interactions among a host population, an insect-vector population, which transmits virus from hosts to hosts, and a vector predator population is proposed based on virus-host, host-vector, and prey (vector)-enemy theories. The model is investigated to explore the indirect effect of natural enemies on host-virus dynamics by reducing the vector densities, which shows the basic reproduction numbers R01 (without predators) and R02 (with predators) that provide threshold conditions on determining the uniform persistence and extinction of the disease in a host population. When the model is absent from predator, the disease is persistent if R01>1; in such a case, by introducing predators of a vector, then the insect-transmitted disease will be controlled if R02<1. From the point of biological control, these results show that an additional predator population of the vector may suppress the spread of vector-borne diseases. In addition, there exist limit cycles with persistence of the disease or without disease in presence of predators. Finally, numerical simulations are conducted to support analytical results.