Physical mechanism of the E_ψ-driven neoclassical current which exists only in asymmetric toroidal systems is clarified.It is found that symmetry-breaking, violating the total angular momentum conservation, changes the direction of flow and heat flux to be damped by the parallel viscosities. The change in the direction depends on the collisionality through the gemetric factor which reflects symmetry-breaking. As a result, in contrast to symmetric toroidal systems, the flow and heat flux due to the radial electric field E_ψ can be damped according to the collisionality in asymmetric toroidal systems.If dominant species such as electrons and primary ions have different collisionalities, there remains a difference between the flows due to E_ψ, hence a parallel current proportional directly to the radial electric field, i.e., the E_ψ-driven current, is generated in asmmetric toroidal systems in spite of the charge neutrality condition.