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In this paper, we apply the multiplicative bias correction (MBC) techniques for von Mises (vM) kernel density estimator in the context of circular data. Some properties of the MBC-vM kernel circular density estimators (bias, variance and mean integrated squared error) are shown. The choice of bandwidth is investigated by adapting the popular cross-validation techniques. The performances of the MBC estimators based on vM kernel are illustrated by a simulation study and real application for circular data. In general, in terms of integrated squared bias (ISB) and integrated squared error (ISE), the proposed estimators outperform the standard vM kernel estimator. [ABSTRACT FROM AUTHOR]