  The Hecke-Clifford superalgebra is a super-analogue of the Iwahori-Hecke
algebra of type A. The classification of its simple modules is done by Brundan,
Kleshchev and Tsuchioka using a method of categorification of affine Lie
algebras. In this paper, we introduce another way to produce its simple modules
with a generalized theory of cellular algebras which is originally developed by
Graham and Lehrer. In our construction the key is that there is a right action
of the Clifford superalgebra on the super-analogue of the Specht module. With
the help of the notion of the Morita context, a simple module of the
Hecke-Clifford superalgebra is made from that of the Clifford superalgebra.
