  In this paper, we present explicit toric construction of moduli space of
quasi maps from $\mathbb{P}^1$ with two marked points to $\mathbb{P}^1 \times
\mathbb{P}^1$, which was first proposed by Jinzenji and prove that it is a
compact orbifold. We also determine its Chow ring and compute its Poincar\'e
polynomial for some lower degree cases.
