Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computing. In this paper, we study a new promising system of superconducting topological surface state topological insulator thin films. We also study the phase diagrams of the model by plotting the Majorana edge states and the density of states in different regions of the phase diagram. Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet p-wave superconductors, which are also confirmed by the phase diagrams. The chiral Majorana edge modes may provide a new route for realizing topological quantum computation.
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