The mirror of a toric Calabi-Yau 3-orbifold is an affine curve usually referred as mirror curve. I will describe a constructible sheaf model for the Fukaya category on this curve by Dyckerhoff-Kapranov. We first identify the B-model category of matrix factorization with this category in the case of affine orbifolds, where the mirror curve is a multiple cover of a pair of pants. By the descent properties on both sides, one can proceed to the general homological mirror symmetry statement by gluing together affine pieces. This talk is based on the joint work with Qingyuan Bai.