For a invertible singularity W and its admissible symmetry group G, Orbifold Landau-Ginzburg mirror symmetry conjecture states that a quantum singularity theory (A model) of (W, G) is equivalent to another different theory (B model) of different  singularity W^T and symmetry G^T. In this talk, I will describe a Frobenius algebra version of LG mirror symmetry, including totally different ways to construct Frobenius algebra structure from A and B model side via derived category of matrix factorization, and a mirror theorem about the isomorphism of the two different Frobenius algebra structure in the case W is Fermat or loop type. This is part of the joint work in progress with Polishchuk, Vaintrob and Shen.