  We describe a class (called regular) of invariant generalized complex
structures on a real semisimple Lie group G. The problem reduces to the
description of admissible pairs (\gk, \omega), where \gk is an appropriate
regular subalgebra of the complex Lie algebra \gg^{C} associated to G and
\omega is a closed 2-form on \gk, such that a non-degeneracy condition holds.
  In the case when G is a semisimple Lie group of inner type (in particular,
when G is compact) a classification of regular generalized complex structures
on G is given. We show that any invariant generalized complex structure on a
compact semisimple Lie group G is regular, provided that an additional natural
condition holds.
  In the case when G is a semisimple Lie group of outer type, we describe the
subalgebras \gk in terms of appropriate root subsystems of a root system of
\gg^{C} and we construct a large class of admissible pairs (\gk ,\omega)
(hence, regular generalized complex structures on G).
