Ce$_{3}$Al is an archetypal heavy-fermion compound with multiple crystalline phases. Here, we try to investigate its electronic structures in the hexagonal phase ($alpha$-Ce$_{3}$Al) and cubic phase ($beta$-Ce$_{3}$Al) by means of a combination of density functional theory and single-site dynamical mean-field theory. We confirm that the 4$f$ valence electrons in both phases are itinerant, accompanied with strong valence state fluctuations. Their 4$f$ band structures are heavily renormalized by electronic correlations, resulting in large effective electron masses. The Kondo screening in Ce$_{3}$Al would be protracted over a wide range of temperature since the single-impurity Kondo temperature $T_{K}$ is much higher than the coherent Kondo temperature $T^{*}_{K}$. Especially, the crystal structure of $alpha$-Ce$_{3}$Al forms a layered kagome lattice. We observe conspicuous kagome-derived flat bands and Dirac cones (or gaps) in its quasiparticle band structure. Therefore, it is concluded that the hexagonal phase of Ce$_{3}$Al will be a promising candidate of heavy-fermion kagome metal.
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