We study the problem of constructing explicit sparse imbalanced bipartite unique-neighbor expanders. For large enough $d_1$ and $d_2$, we give a strongly explicit construction of an infinite family of $(d_1,d_2)$-biregular graph (assuming $d_1 \leq d_2$) where all sets $S$ with fewer than $1/d_1^3$ fraction of vertices have $\Omega(d_1\cdot |S|)$ unique-neighbors. Further, for each $\beta\in(0,1)$, we give a construction with the additional property that the left side of each graph has roughly $\beta$ fraction of the total number of vertices. Our work provides the first two-sided construction of imbalanced unique-neighbor expanders, meaning small sets contained in both the left and right side of the bipartite graph exhibit unique-neighbor expansion. Our construction is obtained from the ``line product'' of a large small-set edge expander and a sufficiently good constant-sized unique-neighbor expander, a product defined in the work of Alon and Capalbo.