Abstract: The quantum phases of many-body polaron was investigated in two-dimensional optical lattices in Mott Insulator regime. The polaron is a quasi-particle formed by the coupling between bosons in optical lattices and BEC phonons. The effective Hamiltonian of polarons is derived through Lang-Firsov transformation. The system can be described by extended Bose-Hubbard Model. In Mott Insulator regime, the Hamiltonian was solved directly so that the quantum phases of the system can be obtained for single-component case with filling factors of 1/2 and 1/4. By using Hartree-Fock approximation, more quantum phases for two-component case with filling factors of 1/2 and 1/4 can be found. Non-trivial quantum phases was predicted in single-component and two-component systems of polarons.