Step 1: Assign oxidation state of oxygen.
Oxidation state of oxygen is $-2$. Step 2: Let oxidation state of vanadium be $x$.
There are 2 vanadium atoms and 7 oxygen atoms in the ion. Step 3: Write the oxidation number equation.
\[
2x + 7(-2) = -4
\]
\[
2x - 14 = -4
\]
\[
2x = 10
\]
\[
x = +5
\] Step 4: Conclusion.
The oxidation number of vanadium in $V_2O_7^{4-}$ ion is $+5$.