To improve the drilling system voltage stability level and prevent taking place the collapse of voltage, the bifurcation theory is adopted to research the voltage stability problem in oil field drilling system. The model of generator, loads and drilling system is established separately, then general model of voltage stability analysis in drilling system is obtained, bifurcation phenomenon in power grid is analyzed, at last dynamic and static voltage bifurcation points of electric system are simulated and searched. On the basis, the voltage instability analysis in successive stage is undertaken by making use of reactive power of generators. Results show that system voltage loses stability up to collapse in static bifurcation and generates oscillations in dynamic bifurcation. The results are in favor of inquiring operating characteristic in drilling system deeply, and play an active role in maintaining system voltage stability.