  In the first part of this paper we investigate the operator aspect of
higher-rank supersymmetric model which is introduced as a Lie theoretic
extension of the $N=2$ minimal model with the simplest case $su(2)$
corresponding to the $N=2$ minimal model.
  In particular we identify the analogs of chirality conditions and chiral
ring. In the second part we construct a class of topological conformal field
theories starting with this higher-rank supersymmetric model. We show the
BRST-exactness of the twisted stress-energy tensor, find out physical
observables and discuss how to make their correlation functions. It is
emphasized that in the case of $su(2)$ the topological field theory constructed
in this paper is distinct from the one obtained by twisting the $N=2$ minimal
model through the usual procedure.
