For　linear　systems,　the　original　Kalman　filter　under　the　minimum　mean　square　error　(MMSE)　criterion　is　an　optimal　filter　under　a　Gaussian　assumption.　However,　when　the　signals　follow　non-Gaussian　distributions,　the　performance　of　this　filter　deteriorates　significantly.　An　efficient　way　to　solve　this　problem　is　to　use　the　maximum　correntropy　criterion　(MCC)　instead　of　the　MMSE　criterion　to　develop　the　filters.　In　a　recent　work,　the　maximum　correntropy　Kalman　filter　(MCKF)　was　derived.　The　MCKF　performs　very　well　in　filtering　heavy-tailed　non-Gaussian　noise,　and　its　performance　can　be　further　improved　when　some　prior　information　about　the　system　is　available　(e.g.,　the　system　states　satisfy　some　equality　constraints).　In　this　paper,　to　address　the　problem　of　state　estimation　under　equality　constraints,　we　develop　a　new　filter,　called　the　MCKF　with　state　constraints,　which　combines　the　advantages　of　the　MCC　and　constrained　estimation　technology.　The　performance　of　the　new　algorithm　is　confirmed　with　two　illustrative　examples.