  In this paper, for quasi-split classical groups over p-adic fields, we
determine the L-packets consisting of simple supercuspidal representations and
their corresponding L-parameters, under the assumption that p is not equal to
2. The key is an explicit computation of characters of simple supercuspidal
representations and the endoscopic character relation, which is a
characterization of the local Langlands correspondence for quasi-split
classical groups.
