We demonstrate a method for controlling strong chaos by an aperiodic perturbation in two-dimensionalHamiltonian systems. The method has the advantages that the controlled system remains conservative property and theselection of the perturbation has a considerable diversity. We illustrate this method with two area preserving maps: thenon-monotonic twist map which is a mixed system and the perturbed cat map which exhibits hard chaos. Numericalresults show that the strong chaos can be effectively controlled into regular motions, and the final states are alwaysquasiperiodic ones. The method is robust against the presence of weak external noise.