In this letter, we first investigate some new properties of a known power residue frequency-hopping sequence (FHS) set which is established as an optimal one-coincidence frequency-hopping sequence (OC-FHS) set with near-optimal set size. Next, combining the mathematical structure of power residue theory with interleaving technique, we present a new class of optimal OC-FHS set, using the Chinese Remainder Theorem (CRT). As a result, one optimal OC-FHS set with prime length is extended to another optimal OC-FHS set with composite length in which the construction preserves the maximum Hamming correlation (MHC) and the set size as well as the optimality of the Lempel-Greenberger bound.