Manipulation of spin-flip is important in spintronics applications. In this paper, we report a simple manipulation of three Co-3d spin states in the Co3O4 spinel. From first principles calculations, we demonstrate that the spin state of Co atoms at octahedral sites (Co-oct) of the Co3O4 spinel can be manipulated through tensile stains. The magnetic moment of the Co-oct changes from the ground non-magnetic (0 A mu (B)) state to the intermediate-spin state (2 mu (B)) and high-spin state (4 mu (B)) when 5 % (or higher) uniaxial tensile strain and 3 % (or higher) biaxial tensile strain are applied to the lattice, respectively. Moreover, the mechanism of the spin state transition of the Co-3d electrons in Co3O4 is discussed, and we show that the occurrence of spin-flip is a result of the competition between the cubic crystal field energy and the exchange correlation energy. These results open a new route to achieve and manipulate triple-spin states in spintronic devices.