A selective one-way wrench includes a head defining a first space and a second space communicated with the first space. A gear is put pivotally in the first space. The gear includes a toothed external face. A direction controller is put in the second space. The direction controller includes two toothed faces. A spring pushes the direction controller to the gear. A direction switch includes a first element put pivotally on the head and a second element put in the second space and connected to the first element for bringing selected one of the toothed faces of the direction controller into engagement with the toothed external face of the gear.