Spin-orbit torque (SOT) manipulation of perpendicular magnetization is essential for realizing spintronic storage and logic devices. When a charge current flows through a heavy metal/ferromagnetic layer structure, a spin current can be generated by the heavy metal and injects into the ferromagnetic layer with perpendicular magnetic anisotropy and switch its magnetization via the SOT. However, in order to realize the deterministic switching, an in-plane external magnetic field is needed to break the inversion symmetry, a technological requirement that hampers the practical application of SOT. Pt/Co multilayer is a good magnetic recording media and, thus, the all-electric manipulation of its perpendicular magnetic moments is of practical significance. The noncollinear spin structure in Mn3Sn allows an unconventional spin polarization direction, and the associated SOT can switch the magnetic moments in the absence of an external field. In this work, we demonstrate the field-free SOT switching of a heterostructure utilizing Mn3Sn and Pt/Co multilayer as the spin source and the ferromagnetic layer with perpendicular magnetization, respectively. Our results are important for advancing the development of spintronic devices based on noncollinear antiferromagnets.