  We study the three-dimensional gravity with torsion given by the
Mielke-Baekler (MB) model coupled to gravitational Chern-Simons term, and that
possess electric charge described by Maxwell-Chern-Simons electrodynamics. We
find and discuss this theory's charged black holes solutions and uncharged
solutions. We find that for vanishing torsion our solutions by means of a
coordinate transformation can be written as three-dimensional Chern-Simons
black holes. We also discuss a special case of this theory, Topologically
Massive Gravity (TMG) at chiral point, and we show that the logarithmic
solution of TMG is also a solution of the MB model at a fixed point in the
space of parameters. Furthermore, we show that our solutions generalize Godel
type solutions in a particular case. Also, we recover BTZ black hole in
Riemann-Cartan spacetime for vanishing charge.
