The　LC　circuit　with　a　nonlinear　capacitor　is　analyzed　using　the　symplectic　conservative　perturbation　method　based　on　the　symplectic　matrix.　By　treating　the　electric　charge　and　the　flux　linkage　as　dual　variables,　the　LC　circuit　system　can　be　transformed　into　a　Hamiltonian　system.　Then　we　solve　the　nonlinear　Hamiltonian　matrix　equation　by　the　perturbation　method.　The　Hamiltonian　matrix　can　be　cast　into　linear　and　nonlinear　parts.　Based　on　the　exact　solution　of　the　linear　part,　the　nonlinear　part　is　solved　perturbatively　by　a　canonical　transformation.　Since　the　coefficient　matrix　of　the　obtained　equation　is　still　a　Hamiltonian　matrix,　symplectic　conservation　is　guaranteed.　The　validity　of　the　method　is　demonstrated,　and　the　stability,　precision,　and　the　efficiency　of　the　method　are　discussed　by　comparing　it　with　the　fourth-order　Runge-Kutta　method　(RK4),　the　ordinary　perturbation　method,　the　small-parameter　perturbation　method　based　on　displacement　(SPPD),　and　the　harmonic　balance　(HB)　method.　Numerical　results　show　that　the　proposed　method　has　better　stability,　precision,　and　efficiency　compared　with　the　other　methods　and　thus　has　great　advantages　in　long-term　simulations.