We systematically synthesized perovskite-type oxides Sr_1−xCa_xCoO₃ containing unusually high valence Co⁴⁺ ions by a high pressure technique and investigated the effect of systematic lattice change on the magnetic and electronic properties. As the Ca content x exceeds about 0.6, the structure changes from cubic to orthorhombic, which is supported by the first-principles calculations of enthalpy. Upon the orthorhombic distortion, the ground state remains to be apparently ferromagnetic, with a slight drop of the Curie temperature. Importantly, the compounds with x larger than 0.8 show antiferromagnetic behavior, with positive Weiss temperatures and nonlinear magnetization curves at the lowest temperature, implying that the ground state is non-collinear antiferromagnetic or helimagnetic. Considering the incoherent metallic behavior and the suppression of the electronic specific heat at the high x region, the possible emergence of a helimagnetic state in Sr_1−xCa_xCoO₃ is discussed in terms of the bandwidth narrowing and the double-exchange mechanism with the negative charge transfer energy, as well as the spin frustration, owing to the next-nearest neighbor interaction.