Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. Here by using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe1-xSex (x = 0.45, superconducting transition temperature Tc = 14.5 K) hosts Dirac-cone type spin-helical surface states at Fermi level; the surface states exhibit an s-wave superconducting gap below Tc. Our study shows that the surface states of FeTe0.55Se0.45 are 2D topologically superconducting, providing a simple and possibly high temperature platform for realizing Majorana states.