Summary: In this study we are concerned about the exponential stability of the semigroup associated with a linear viscoelastic wave equation with a locally distributed damping. We will use the method developed by Z. Liu and S. Zheng [Semigroups associated with dissipative systems. Boca Raton, FL: Chapman & Hall/ CRC (1999; Zbl 0924.73003)]. This method is very different from some others in the literature, such as the traditional energy method, see J. E. Muñoz Rivera [Funkc. Ekvacioj, Ser. Int. 35, No. 1, 19–30 (1992; Zbl 0838.73006)], Kormonik’s method, see V. Komornik and E. Zuazua [J. Math. Pures Appl. (9) 69, No. 1, 33–54 (1990; Zbl 0636.93064)] and Nakao’s method, see M. Nakao [Math. Z. 193, 227–234 (1986; Zbl 0658.35064)].