Let $σ$ be a permutation on $n$ letters. We say that a permutation $τ$ is an even (resp. odd) $k$th root of $σ$ if $τ^k=σ$ and $τ$ is an even (resp. odd) permutation. In this article, we obtain generating functions for the number of even and odd $k$th roots of permutations. Our result implies know generating functions of Moser and Wyman and also some generating functions for sequences in The On-line Encyclopedia of Integer Sequences (OEIS).