An implicit flux-corrected transport (FCT) algorithm is developed for a class of chemotaxis models. The coefficients of the Galerkin finite element discretization are adjusted in such a way as to guarantee mass conservation and keep the cell density nonnegative. The numerical behaviour of the proposed high-resolution scheme is tested on the blow-up problem for an minimal chemotaxis model with singularities. It is also shown that the results for an Escherichia coli chemotaxis model are in good agreement with experimental data reported in the literature.