In this paper, we first present a combinatorial proof of the recurrence relation about the number of the inverse-conjugate compositions of \(2n+1\), \(n > 1\). And then we get some counting results about the inverse-conjugate compositions for special compositions. In particular, we show that the number of the inverse-conjugate compositions of \(4k+1\), \(k > 0\) with odd parts is \(2^k\), and provide an elegant combinatorial proof. Lastly, we give a relation between the number of the inverse-conjugate odd compositions of \(4k+1\) and the number of the self-inverse odd compositions of \(4k+1\).