This　paper　presents　a　robust　3D　point　cloud　registration　algorithm　based　on　bidirectional　Maximum　Correntropy　Criterion　(MCC).　Comparing　with　traditional　registration　algorithm　based　on　the　mean　square　error　(MSE),　using　the　MCC　is　superior　in　dealing　with　complex　registration　problem　with　non-Gaussian　noise　and　large　outliers.　Since　the　MCC　is　considered　as　a　probability　measure　which　weights　the　corresponding　points　for　registration,　the　noisy　points　are　penalized.　Moreover,　we　propose　to　use　bidirectional　measures　which　can　maximum　the　overlapping　parts　and　avoid　the　registration　result　being　trapped　into　a　local　minimum.　Both　of　these　strategies　can　better　apply　the　information　theory　method　to　the　point　cloud　registration　problem,　making　the　algorithm　more　robust.　In　the　process　of　implementation,　we　integrate　the　fixed-point　optimization　technique　based　on　the　iterative　closest　point　algorithm,　resulting　in　the　correspondence　and　transformation　parameters　that　are　solved　iteratively.　The　comparison　experiments　under　noisy　conditions　with　related　algorithms　have　demonstrated　good　performance　of　the　proposed　algorithm.