An f -coloring of a graph G is an edge-coloring of G such that each color appears at each vertex v ∈ V ( G ) at most f ( v ) times. The minimum number of colors needed to f -color G is called the f -chromatic index of G . A simple graph G is of f -class 1 if the f -chromatic index of G equals Δ f ( G ) , where Δ f ( G ) = max v ∈ V ( G ) { ⌈ d G ( v ) ∕ f ( v ) ⌉ } . In this article, we find a new sufficient condition for a simple graph to be of f -class 1, which is strictly better than a condition presented by Zhang et. al (2010). As a consequence, this result extends earlier results of Hakimi and Schmeichel, Hoffman and Rodger, Akbari, Cariolaro, Chavooshi, Ghanbari and Zare on class 1 graphs.