The phase relationship of Re-alloyed Ru2Si3 and the variations of the crystal structures and thermoelectric properties of the Ru1-xRexSiy chimney-ladder phases have been studied as a function of the Re concentration. The Ru1-xRexSiy chimney-ladder phases are formed in a wide compositional range. Compositional formula of the chimney-ladder phases are determined to be Ru1-xRexSi1.5386+0.1783x (0.14 ≤ x ≤ 0.76), which are systematically deviated from the idealized composition conforming the valence electron counting rule: VEC=14. Measurements of thermoelectric properties of single crystals with different compositions reveals that the chimney-ladder phases exhibit n-type semiconducting behavior at low Re concentrations and p-type semiconducting behavior at high Re concentrations. These results suggests that the VEC=14 rule can be used for predicting the semiconducting behavior of the chimney-ladder phases through the adjustment of VEC values by substituting elements, producing p-type semiconductors for VEC<14 and n-type for VEC>14, with the carrier concentration related to the deviation from VEC=14.