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The Landau damping which reveals the characteristic of relaxation dynamics for an equilibrium state is a universal concept in the area of complex system.In this paper,we study the Landau damping in the phase oscillator system by considering two types of coupling heterogeneity in the Kuramoto model.We show that the critical coupling strength for phase transition,which can be obtained analytically through the balanced integral equation,has the same formula for both cases.The Landau damping effects are further explained in the framework of Laplace transform,where the order parameters decay to zero in the long time limit.