  We study 2D Maxwell-dilaton gravity on AdS(2). We distinguish two distinctive
cases depending on whether the AdS(2) solution can be lifted to an AdS(3)
geometry. In both cases, in order to get a consistent boundary condition we
need to work with a twisted energy momentum tensor which has non-zero central
charge. With this central charge and the explicit form of the twisted Virasoro
generators we compute the entropy of the system using the Cardy formula. The
entropy is found to be the same as that obtained from gravity calculations for
a specific value of the level of the U(1) current. The agreement is an
indication of $AdS(2)/CFT(1) correspondence.
