Neural　networks　have　found　widespread　application　in　medical　image　registration,　although　they　typically　assume　access　to　the　entire　training　dataset　during　training.　In　clinical　scenarios,　medical　images　of　various　anatomical　targets,　such　as　the　heart,　brain,　and　liver,　may　be　obtained　successively　with　advancements　in　imaging　technologies　and　diagnostic　procedures.　The　accuracy　of　registration　on　a　new　target　may　degrade　over　time,　as　the　registration　models　become　outdated　due　to　domain　shifts　occurring　at　unpredictable　intervals.　In　this　study,　we　introduce　a　deep　registration　model　based　on　continual　learning　to　mitigate　the　issue　of　catastrophic　forgetting　during　training　with　continuous　data　streams.　To　enable　continuous　network　training,　we　propose　a　dynamic　memory　system　based　on　a　density-based　clustering　algorithm　to　retain　representative　samples　from　the　data　stream.　Training　the　registration　network　on　these　representative　samples　enhances　its　generalization　capabilities　to　accommodate　new　targets　within　the　data　stream.　We　evaluated　our　approach　using　the　CHAOS　dataset,　which　comprises　multiple　targets,　such　as　the　liver,　left　kidney,　and　spleen,　to　simulate　a　data　stream.　The　experimental　findings　illustrate　that　the　proposed　continual　registration　network　achieves　comparable　performance　to　a　model　trained　with　full　data　visibility.