End-to-end　network　slicing,　as　a　key　technology　in　5G　and　B5G　mobile　communication　systems,　is　to　enable　traditional　wireless　networks　to　support　different　services　in　vertical　industries.　In　a　heterogeneous　cellular　network　(HetNets)　with　network　slicing　functions,　due　to　the　dense　deployment　of　base　stations　(BSs)　and　the　mobility　of　user　equipments　(UEs),　dynamically　switching　network　slices　(NSs)　is　necessary　for　better　system　performance.　This　paper　models　the　handoff　problem　of　end-to-end　NS　as　a　Markov　decision　process　(MDP)　maximizing　the　utility　related　to　the　UE＇s　profit　of　being　served,　the　handoff　cost　and　the　outage　penalty.　Both　the　states　of　the　radio　access　network　resources　and　the　core　network　resources　of　each　end-to-end　NS　are　considered.　The　deep　reinforcement　learning　(DRL)　is　adopted　as　the　solution,　and　a　double　deep　Q　network　(DQN)　based　NS　handoff　algorithm　is　designed.　Numerical　results　confirm　the　convergence　of　the　DQN　used　to　make　handoff　decisions　and　show　that　compared　with　typical　handoff　algorithms,　the　algorithm　we　proposed　performs　the　best　from　the　aspect　of　the　cumulative　reward　designed　in　this　paper.