Kagome materials have become solid grounds to study the interplay among geometry, topology, correlation, and magnetism. Recently, semiconductors Nb3X8(X = Cl, Br, I) have been predicted to be two-dimensional (2D) magnets and importantly these materials possess breathing kagome geometry. Electronic structure study of these promising materials is still lacking. Here, we report the spectroscopic evidence of flat and weakly dispersing bands in breathing-kagome semiconductor Nb3I8 around 500 meV binding energy, which is well supported by our first-principles calculations. These bands originate from the breathing kagome lattice of Niobium atoms and have Nb d character. They are found to be sensitive to polarization of the incident photon beam. Our study provides insight into the electronic structure and flat band topology in an exfoliable kagome semiconductor thereby providing an important platform to understand the interaction of geometry and electron correlations in 2D material.