The effect of three kinds of anti-site disorder to electronic structure and magnetic properties of the LiMgPdSb-type CoMnTiSi alloy are investigated. It was found the Mn-Ti anti-site disorder can induce the diluted magnetism in CoMnTiSi matrix. The magnetic structure has an oscillation between the ferromagnetic and antiferromagnetic states with the different degree of Mn-Ti anti-site disorder. Two novel characteristics: the diluted antiferromagnetic half-metallicity and the diluted zero-gap half-metallity are found in the different degree range of the Mn-Ti anti-site disorder. The Co-Mn and Co-Ti anti-site disorder have little effect on the magnetic properties. The width of energy gap and the intensity of DOS at the Fermi level can be adjusted by the degree of Co-Mn or Co-Ti anti-site disorder. The independent control to the carrier concentration and magnetization can be realized by introducing the different anti-site disorder.