In this paper, we study a Cauchy problem for quasilinear wave equations with dissipative term in Sobolev space H^L × H^L-1 (L ≥ [d/2] + 3). The coefficients of the dissipative term depends on space variables and may vanish in some compact region. In order to control the derivatives of the dissipative coefficients, we introduce a rescaling argument. Using the argument, we obtain a global existence theorem and decay estimates with additional assumptions for the initial data.