Topological insulators (TIs) are exotic materials which have topologically protected states on the surface due to strong spin-orbit coupling. However, a lack of ordered growth of TI thin films on amorphous dielectrics and/or insulators presents a challenge for applications of TI-junctions. We report the growth of topological insulator Bi2Se3 thin films on amorphous SiO2 by molecular beam epitaxy (MBE). To achieve the ordered growth of Bi2Se3 on an amorphous surface, the formation of other phases at the interface is suppressed by Se passivation. Structural characterizations reveal that Bi2Se3 films are grown along the [001] direction with a good periodicity by the van der Waals epitaxy mechanism. A weak anti-localization effect of Bi2Se3 films grown on amorphous SiO2 shows a modulated electrical property by the gating response. Our approach for ordered growth of Bi2Se3 on an amorphous dielectric surface presents considerable advantages for TI-junctions with amorphous insulator or dielectric thin films.