Memristive　nonlinear　system　has　drawn　much　attention　in　recent　years,　due　to　its　rich　and　complex　dynamical　characteristics.　However,　there　are　few　studies　focus　on　the　analytical　analysis　of　this　significant　system.　In　this　paper,　a　novel　analytical　method　for　analyzing　the　chaotic　trajectories　of　memristive　circuit　is　proposed.　This　method　combines　Homotopy　Analysis　Method　(HAM)　and　Multi-objective　Optimization　(MO),　i.e.,　the　convergence　control　parameter　of　traditional　HAM　is　divided　into　lots　of　subintervals　in　the　time　domain　and　respectively　optimized　by　MO,　for　accurately　solving　the　Ordinary　Differential　Equations　describing　memristive　circuits.　Hence,　this　method　is　named　by　MO-based　multi-interval　HAM　(MO-MIHAM).　By　using　MO-MIHAM,　we　accurately　tracked　the　chaotic　trajectories　of　the　classical　Memristor-Capacitor-Inductor　(MCL)　circuit　and　current　memristive　Band　Pass　Filter　(BPF)　chaotic　circuit.　Furthermore,　based　on　the　comparisons　of　errors　between　analytical　approximate　solutions　derived　from　MO-MIHAM　and　solutions　solved　by　traditional　homotopy-based　analytical　methods　and　by　Runge-Kutta-Fehlberg　Method　(RKF45)　based　numerical　analysis,　we　found　that,　MO-MIHAM　is　characterized　by　higher　approximation　accuracy　and　computational　performance　(comprehensively　considering　the　accuracy,　computational　complexity　and　execution　time　by　a　proposed　Quality　Factor)　among　the　homotopy-based　analytical　methods,　due　to　the　optimized　convergence　control　parameters　in　subintervals.　Besides　this　major　advantage,　MO-MIHAM　enables　both　qualitative　and　quantitative　analyses　and　high　freedom　to　choose　homotopy-related　terms　for　simplicity,　and　it　is　insensitive　to　convergence　issues.　Therefore,　it　is　a　powerful　tool　for　exploratory　studies　for　analytically　analyzing　chaotic　dynamics　in　memristive　circuit.