Let $C_n$ be an $n$-dimensional cross-polytope and ${\mathrm{\Gamma }}_p(C_n)$ be the smallest positive number $\gamma$ such that $C_n$ can be covered by $p$ translates of $\gamma C_n$. We obtain better estimates of ${\mathrm{\Gamma }}_{2^n}(C_n)$ for small $n$ and a universal upper bound of ${\mathrm{\Gamma }}_{2^n}(C_n)$ for all positive integers $n$.