The　dynamic　modeling　problem　for　the　flexible　two-wheel　upright　self-balance　humanoid　robot　is　tackled.　A　dynamic　model　for　the　flexible　two-wheel　self-balance　humanoid　robot　is　obtained　based　on　Lagrange　equation　and　dynamics　theory.　Spring　is　used　to　imitate　hominine　lumbar　spine　and　flexible　lumbar　curvature　of　the　robot　is　considered,　which　are　different　from　previous　robots.　The　gained　dynamics　model　is　linearized　and　its　state-space　equations　are　established.　The　structure　of　the　established　dynamic　model　is　very　simple,　and　it　is　easy　to　control　the　robot　effectively.　Simulation　results　prove　the　system　stability,　and　experiment　results　are　analyzed　in　detail,　verifying　that　the　system　modeling　and　the　linear-quadraic　regulator　(LQR)　controller　design　are　valid　and　rational.