Divergence structure for the quantum entropy of a black hole in Anti-de Sitter spacetime due to the electromagnetic and gravitational fields is investigated by using the brick-wall model. The entropy has both linearly and logarithmically divergent terms, where the linearly divergent term can reduce to the form proportional to the event horizon area if the temperature is replaced by the Hawking temperature and the coordinate cutoff is replaced by the proper cutoff; while the logarithmic divergences not only depend on the characteristics of the black hole but also on the spin of the fields. Since this term exists, the contribution of a spin field in general is not proportional to the scalar one.