Department of Mathematics, Hooghly Mohsin College,Chinsurah-712101, Hooghly, India A system of non-linear differential equations is proposed as a predator-prey mathematical model with disease in both prey and predator. Total population is divided into four groups, namely susceptible prey, infected prey, susceptible predatorand infected predator. The dynamical behavior of this system about each of the equilibrium points has been observed. The system locally asymptotically stable at the interior equilibrium point is observed. It has been also observed that a Hopf- bifurcation can happen about the interior equilibrium point when the rate of infection crosses some parameter threshold. The analytical findings are supported by the numerical observations.