Memristive　networks　are　large-scale　non-linear　circuits　based　on　memristor　cells,　playing　a　crucial　role　in　developing　the　emerging　researches　such　as　next-generation　artificial　intelligence,　bioelectronics,　and　high-performance　memory.　The　performance　of　memristive　networks　is　greatly　affected　by　the　memristor　model　describing　physical　and　electrical　characteristics　of　a　memristor　cell.　However,　existing　models　are　mainly　nonanalytic　and,　accordingly,　may　have　convergence　issues　in　their　applications　in　memristive　networks＇　analyses.　Therefore,　aiming　at　improving　convergence　of　memristive　networks,　we　propose　an　analytic　modeling　strategy　for　memristor　based　on　homotopy　analysis　method　(HAM).　In　this　strategy,　the　HAM　is　used　to　obtain　an　analytic　memristor　model　through　solving　the　state　equations　of　memristors　in　original　physical　model.　Specifically,　the　HAM　is　used　to　solve　the　analytic　approximate　solution　of　the　core　parameter　of　memristor　state　variable,　from　the　state　equations,　in　the　form　of　analytic　homotopy　series.　Then　the　analytic　approximate　model　of　memristor　is　obtained　by　using　the　solved　state　variables.　The　characteristics　of　the　proposed　strategy　are　as　follows.　1)　Its　solution　has　a　closed-form　expression,　i.e.　an　explicit　function,　2)　its　approximation　error　is　optimized,　thereby　realizing　the　convergence　optimization.　Moreover,　according　to　the　characteristics　of　memristive　networks,　we　introduce　an　analysis　criterion　for　memristor　model　applicable　to　memristive　networks.　Through　the　long-time　evolution　experiments　of　a　memristor　cell　and　a　benchmark　memristive　matrix　network　with　different　inputs,　and　the　comparisons　with　the　traditional　non-analytic　(numeric)　method,　we　verify　the　analyticity　and　convergence　superiority　of　the　modeling　strategy.　Besides,　based　on　this　strategy　and　the　comparison　experiments,　we　reveal　that　one　of　the　underlying　reasons　for　nonconvergence　in　the　large-scale　memristive　network　simulation　possesses　the　non-analyticity　of　the　used　memristor　model.　The　strategy　can　be　further　used　for　analyzing　the　performances　of　a　memristor　cell　and　memristive　networks　in　long-time.　It　also　has　potential　applications　in　emerging　technologies.