Despite the simple crystal structure, LiFeAs having nontrivial band structure and anisotropy of superconducting properties seems the most exotic compound among iron-based superconducting pnictides. Nonetheless, the available experimental studies are not so numerous due to LiFeAs chemical instability even in presence of a trace amount of water vapors or oxygen. Here, using the Andreev spectroscopy of break junctions in LiFeAs single crystals, we unambiguously show a coexistence of three superconducting condensates below critical T_c = 17 K. The temperature dependences of the order parameters and the anisotropy of the middle and the large gaps, as well as the excess Andreev current, and zero-bias conductance are directly measured. We estimate the partial band contributions to the total conductance. Additionally, considered is an influence of the band structure topology near the Fermi level on the dynamic conductance in the Andreev regime.