High-index Bi2Se3(221) has been successfully grown on partially suspended Ga2Se3(001). The Ga2Se3 layer was formed by selenation of GaSb(001) surface, which revealed a suspended structure supported only by some GaSb nano-pillars. Such a growth behavior may be beneficial for achieving heterostructures with large lattice misfits and suppressing the coupling between the substrate and deposit. Bi2Se3, a typical topological insulator, has been grown on Ga2Se3 along the high-index [221] direction despite of the large lattice mismatch.