An　attitude　controller　with　finite　time　convergence　rate　for　satellite　attitude　tracking　issue　considering　the　flexible　dynamic　based　on　a　finite　time　modal　state　observer　is　proposed　in　this　article.　The　deformation　of　flexible　appendages　is　taken　into　consideration　and　a　finite-time　state　observer　with　auxiliary　state　to　offset　the　initial　error　is　proposed　to　get　the　flexible　vibration　estimation.　The　modal　state　and　its　derivative　could　be　estimated　by　a　full　dimensional　feedback　observer.　A　finite　time　sliding　mode　based　on　the　fraction　order　feedback　of　MRP　is　constructed　and　the　finite　time　controller　is　proposed.　The　modal　estimation　is　implied　in　controller　design　hence　the　counteraction　of　flexible　system　could　be　offset.　System　global　finite-time　stability　is　proved　by　Lyapunov　method　and　the　superiority　is　demonstrated　by　simulation　results.