Super-high resolution laser-based angle-resolved photoemission measurements are carried out on LiFeAs superconductor to investigate its electron dynamics. Three energy scales at ～ 20 meV, ～ 34 meV, and ～ 55 meV are revealed for the first time in the electron self-energy both in the superconducting state and normal state. The ～ 20 meV and ～ 34 meV scales can be attributed to the coupling of electrons with sharp bosonic modes which are most likely phonons. These observations provide definitive evidence on the existence of mode coupling in iron-based superconductors.