We studied the atomic and electronic structures of ultrathin Bi(111) films grown on Bi(2)Te(3) by means of angle-resolved photoemission, first-principles calculations, and low-energy electron diffraction. These Bi films were found to be strained due to the influence of the substrate. Accordingly, the band structure is affected and Bi undergoes a topological phase transition; it is shown that the Z(2) topological invariant in three dimensions switches from +1 (trivial) to -1 (nontrivial or topological). This was clearly confirmed from the change in the surface-state dispersion near the Fermi level. Our discovery offers a method to produce novel topological systems from simple materials.