In pressing a slack-side span 16a of a V-ribbed belt 16, entrained about a crank pulley 1 variable in rotational speed, auxiliary pulleys 4, 7 and 10 and an idler pulley 13, with an auto tensioner 24, thereby automatically balancing tension of the belt, the damping coefficient DI of the auto tensioner 24 is set in accordance with the modulus of longitudinal elasticity of the belt 16. For example, when the modulus of longitudinal elasticity of the belt 16 is at least 9800 N/100% rib and less than 29400 N/100% rib, the damping coefficient DI of the auto tensioner 24 is set at at least 20% and less than 100%. In this manner, even if the rate at which the auto tensioner 24 absorbs elongation of the belt 16 is as extremely small as 0.3 to 1.0 mm/deg, a rocking motion of the auto tensioner 24 can be avoided thereby reducing the occurrence of a slip or a frictional sound of the belt 16 and the occurrence of abrasion and frictional sounds of friction members, such as an insert bearing 27 and a thrust washer 33, of the auto tensioner 24.