Altermagnetism is a newly identified fundamental class of magnetism with vanishing net magnetization and time-reversal symmetry broken electronic structure. Probing the unusual electronic structure with nonrelativistic spin splitting would be a direct experimental verification of an altermagnetic phase. By combining high-quality film growth and in situ angle-resolved photoemission spectroscopy, we report the electronic structure of an altermagnetic candidate, α-MnTe. Temperature-dependent study reveals the lifting of Kramers degeneracy accompanied by a magnetic phase transition at T_{N}=267 K with spin splitting of up to 370 meV, providing direct spectroscopic evidence for altermagnetism in MnTe.