  We investigate extremal Reissner-Nordstrom-AdS black holes in
four-dimensional N=2 abelian gauged supergravity. We find a new attractor
equation which is not reduced to the one in the asymptotically flat spacetime.
Focusing on so-called the T^3-model with a single neutral vector multiplet, we
obtain non-supersymmetric extremal Reissner-Nordstrom-AdS black hole solutions
with regular event horizon in the D0-D4 and the D2-D6 charge configurations.
The negative cosmological constant emerges even without the Fayet-Iliopoulos
parameters. Furthermore, we also argue the formal description of the
non-supersymmetric black hole solutions of the T^3-model and the STU-model in
generic configurations.
