  We find an exact nonstatic charged BTZ-like solutions, in ($N$+1)-dimensional
Einstein gravity in the presence of negative cosmological constant and a
nonlinear Maxwell field defined by a power $s$ of the Maxwell invariant, which
describes the gravitational collapse of charged null fluid in an anti-de Sitter
background. Considering the situation that a charged null fluid injects into
the initially an anti-de Sitter spacetime, we show that a black hole form
rather than a naked singularity, irrespective of spacetime dimensions, from
gravitational collapse in accordance with cosmic censorship conjecture. The
structure and locations of the apparent horizons of the black holes are also
determined. It is interesting to see that, in the static limit and when N=2,
one can retrieve 2+1 BTZ black hole solutions.
