Glass transition in supercooled Ga0.15Zn0.15Mg0.7 metallic liquid has been simulated by making use of a constant-pressure molecular dynamics technique via the pairwise interatomic potentials calculated from a self-consistent nonlocal model pseudopotential theory. The structures of liquids and glasses are analyzed through careful examinations of the pair distributions functions, structure factors, and the local ordering units, in comparing with the Zn0.3Mg0.7 and Ga0.3Mg0.7 binary cases. It demonstrates that binary Ga0.3Mg0.7 liquids and glasses show relatively stranger compound formation ability than Zn0.3Mg0.7. Although the partial substitution of Zn by Ga in Zn0.3Mg0.7 alloy leads no significant change in the glass transition temperature, it can produce considerable changes in both chemical and topological short-range orders. Chemically, there is a strong phase separation tendency between Ga and Zn atoms, the Zn-Mg heterocoordination preference can be suppressed to some extent by a stronger Ga-Mg compound formation tendency. Topologically, Ga0.15Zn0.15Mg0.7 alloy first appears to be similar to Ga0.3Mg0.7 at the high-temperature region during cooling, then it behaves more like that of Zn0.3Mg0.7 alloy at the low-temperature region. The addition of Ga also induces a restraint to the five-fold symmetry accompanied by an enhancement of the short-range order characterized by 1422- or 1311-type atomic bonded pairs. These results may provide qualitative explanations to some experimental observations on crystallization products and measured transport properties of the GaxZn0.15-xMg0.7 glasses. This study also provides further understandings of glass transition mechanisms and structural properties for the much more complicated multicomponents glass-forming systems that go beyond both the monatomic and the binary cases.