Abstract A disjunctive logic program under the answer set semantics can be equivalently translated to a normal logic program by the shifting transformation, if the program is head-cycle-free. In this paper, we provide an answer-set-preserving rewriting of a general disjunctive program to a normal program by first applying the unfolding transformation on atoms that prevent the program from being headcycle-free, then shifting the resulting program. Different from other transformations that eliminate disjunctions in answer set programming, the new rewriting is efficient for “almost” head-cycle-free programs, i.e., programs that have only a few atoms that prevent them to be head-cycle-free. Based on the new rewriting, we provide an anytime algorithm to compute answer sets of a disjunctive program by calling solvers for normal logic programs. The experiment shows that the algorithm is efficient for some disjunctive programs. We also extend the rewriting to non-ground answer set programs on finite structures.