The　nonlinearity　characteristics　of　memristor　have　been　widely　employed　in　artificial　intelligence.　However,　existing　studies　do　not　provide　much　attention　to　the　analytic　analysis　of　nonlinearity.　This　paper　presents　an　analytic　approach　to　the　nonlinearity　of　memristor　by　analyzing　the　output　spectrum　based　on　homotopy　analysis　method　(HAM).　The　analytic　spectrum　expressions　obtained　by　this　approach　are　verified　by　the　fingerprints　of　memristor.　It　can　be　simultaneously　revealed　that　one　of　the　potential　sources　of　the　nonlinearity　is　the　large　variation　of　state　variable.　Furthermore,　we　propose　a　mapping　method　based　on　the　obtained　total　harmonic　distortion　(THD)　and　a　new　parameter　-　threshold　frequency　\omega　-{C}　to　investigate　the　relationship　between　the　memristor　transition　(i.e.,　the　transition　of　the　memristor　between　a　nonlinear　resistor　and　a　linear　resistor)　and　the　frequency　of　input　signal.　Especially,　analytic　output　spectrum,　THD,　and　threshold　frequency　\omega　-{C}　can　be　solved　without　complex　mathematical　operations　and,　thus,　compared　with　traditional　works,　the　complexity　of　the　proposed　approach　is　reduced.　©　1963-2012　IEEE.