A power-assisted system is to be assembled to a derailleur-equipped bicycle for providing an auxiliary force to the bicycle. The power-assisted system includes: a microcomputer; a pedaling-rate sensor; a bicycle-speed sensor; a shift-position source; and an auxiliary-force database including data about at least a pedaling rate, a running speed, a current gear ratio and the auxiliary force, for defining a ratio between the running speed and the current gear ratio as a first comparison value, and defining the pedaling rate as a second comparison value wherein an auxiliary-force comparison table is made of levels of the auxiliary force to be output corresponding to the first and second comparison values. The microcomputer uses a determining logic circuit to determine the suitable level of the auxiliary force to be output and control the auxiliary-force providing device to output the auxiliary force in the determined level.