  The matching complex of a simple graph $G$ is a simplicial complex consisting
of the matchings on $G$. Jeli\'c Milutinovi\'c et al. studied the matching
complexes of the polygonal line tilings, and they gave a lower bound for the
connectivity of the matching complexes of polygonal line tilings. In this
paper, we determine the homotopy types of the matching complexes of polygonal
line tilings recursively, and determine their connectivities.
