A search for superconductivity has been performed with (Ga 0.5 Co 0.5 )Sr 2 (Tm 1−x Ca x )Cu 2 O z (0⩽x⩽0.5) and (Ga 1−y Co y )Sr 2 (Tm 0.6 Ca 0.4 )Cu 2 O z (0.5⩽y⩽1.0) compounds synthesized under ambient pressure. Materials are characterized by X-ray diffraction, electrical transport, magnetic susceptibility measurements. The X-ray diffraction pattern reveals that all samples have an orthorhombic Ima2 structure. We find that the Co substitution for Ga results in an increase of the solubility limit of Ca of GaSr 2 (Tm 1−x Ca x )Cu 2 O z , and thereby superconductivity is induced by the co-substitution of Ca for Tm and Co for Ga. Bulk superconductivity with a T c of 35K is observed in a sample with nominal composition of (Ga 0.5 Co 0.5 )Sr 2 (Tm 0.6 Ca 0.4 )Cu 2 O z . The variation of the room-temperature thermoelectric power shows that the carrier concentration on the superconducting planes is sensitive to the substitution of Co for Ga in addition to the Ca substitution for Tm.