Helimagnetic materials are identified as promising for novel spintronic applications. Since helical spin order is manifested as a compromise of competing magnetic exchange interactions, its emergence is limited by unique constraints imposed by the crystalline lattice and the interaction geometries as exemplified by the multiferroic perovskite manganites with large orthorhombic distortion. Here we show that a simple cubic perovskite SrCoO3 with room-temperature ferromagnetism has the potential to host helimagnetic order upon isotropic lattice expansion. Increasing the Ba content x in Sr1-xBaxCoO3 continuously expands the cubic lattice, eventually suppressing the ferromagnetic order near x=0.4 where helimagnetic correlations are observed as incommensurate diffuse magnetic scattering by neutron-diffraction measurements. The emergence of helimagnetism is semiquantitatively reproduced by first-principles calculations, leading to the conjecture that a simple cubic lattice with strong d-p hybridization can exhibit a variety of novel magnetic phases originating from competing exchange interactions.