  We present firstly a four-dimensional spherical symmetric black hole with
small Weyl corrections and find that with increasing Weyl corrections the
region of the event horizon existence for the black hole in the parameter space
increases for the negative Weyl coupling parameter and decreases for the
positive one. Moreover, we also obtain a rotating charged black hole with weak
Weyl corrections by the method of complex coordinate transformation. Our
results show that the sign of Weyl coupling parameter $\alpha$ yields the
different spatial topology of the event horizons for the black hole with its
parameters lied in some special regions in the parameter space. We also analyze
the dependence of the ergosphere on the Weyl coupling parameter $\alpha$ and
find that with the increase of the Weyl corrections the ergosphere in the
equatorial plane becomes thick for a black hole with $\alpha>0$, but becomes
thin in the case with $\alpha<0$, which means that the energy extraction become
easier in the background of a black hole with the positive Weyl coupling
parameter, but more difficult in the background of a black hole with the
negative one.
