  The $\Upsilon$ invariant is a concordance invariant defined by using knot
Floer homology. F\"{o}ldv\'{a}ri gives a combinatorial restructure of it using
grid homology. We extend the combinatorial $\Upsilon$ invariant for balanced
spatial graph using grid homology for balanced spatial graph. Regarding links
as spatial graphs, we give a upper and lower bounds for $\Upsilon$ when two
links are connected by a cobordism. Also we show that the combinatorial
$\Upsilon$ is a concordance invariant for knots.
