Microstructure evolutions in the steady--state growth region of directionally solidified Ti--43Al--3Si (atomic fraction, %) alloy were studied at growth rates of 3---100 μm/s. There are four main phase transitions during directional solidification: L→Ti5Si3, L→α+Ti5Si3, α→α2(Ti3Al)+γ(TiAl) and α2→γ+Ti5Si3, especially, the eutectic reaction of α and Ti5Si3 is the typical solidification behavior. When the growth rate exceeds 20 μm/s, another phase transition of L→γ+Ti5Si3 also happens. With increase of growth rate, the steady--state growth microstructure changes from coarse cells to fine cells, to cellular dendrites and then to dendrites. The Ti5Si3 phase stabilizing $\alpha$ phase distributes in the α matrix at a low growth rate, and in the solidified γ matrix at a relatively high growth rate, which is unfavorable in seeding. When the growth rate is 10 μm/s, the distance needed to reach steady--state region becomes shorter, which is favourable in seeding for the present alloy.