Proportionate-type　adaptive　filtering　(PtAF)　algorithms　have　been　successfully　applied　to　sparse　system　identification.　The　major　drawback　of　the　traditional　PtAF　algorithms　based　on　the　mean　square　error　(MSE)　criterion　show　poor　robustness　in　the　presence　of　impulsive　noises　or　abrupt　changes　because　MSE　is　only　valid　and　rational　under　Gaussian　assumption.　However,　this　assumption　is　not　satisfied　in　most　real-world　applications.　To　improve　its　robustness　under　non-Gaussian　environments,　we　incorporate　the　maximum　correntropy　criterion　(MCC)　into　the　update　equation　of　the　PtAF　to　develop　proportionate　MCC　(PMCC)　algorithm.　The　mean　and　mean　square　convergence　performance　analysis　are　also　performed.　Simulation　results　in　sparse　system　identification　and　echo　cancellation　applications　are　presented,　which　demonstrate　that　the　proposed　PMCC　exhibits　outstanding　performance　under　the　impulsive　noise　environments　.