We prove that the sets of homotopy minimal periods for expanding maps on $n$ -dimensional infra-nilmanifolds are uniformly cofinite,i.e., there exists a positive integer $m_0$ , which depends only on $n$ , such that for any integer $m\ge m_0$ , for any $n$ -dimensional infra-nilmanifold $M$ , and for any expanding map $f$ on $M$ , any self-map on $M$ homotopic to $f$ has a periodic point of least period $m$ , namely, $[m_0,\infty)\subset {\rm HPer}(f)$ . This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.