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A kind of homogeneous reaction-diffusion singular predator-prey model with no-flux boundary condition is considered. By using the abstract simplified Hopf bifurcation theorem due to Yi et al. 2009, we performed detailed Hopf bifurcation analysis of this particular pattern formation system. These results suggest the existence of oscillatory patterns if the system parameters fall into certain parameter ranges. And all these oscillatory patterns are proved to be unstable.