The　evolution　dynamics　of　mode　locking　for　a　solid-state　femtosecond　Yb:KGW　laser　is　demonstrated　and　detected　with　time-stretch　dispersive　Fourier　transform　(DFT)　technique　for　the　first　time,　to　the　best　of　our　knowledge.　The　Yb:KGW　laser　is　constructed　first　with　a　classical　X-shaped　cavity,　and　SESAM-assisted　Kerr　lens　mode　locking　is　obtained.　Then,　a　DFT　device　is　built　to　record　the　buildup　and　extinction　dynamics　of　the　mode-locked　laser.　The　results　suggest　that　the　time　of　extinction　is　slightly　shorter　than　the　buildup　time　and　both　of　them　experience　complex　transitions.　The　results　indicate　that　DFT　could　also　be　suitable　to　detect　the　transient　buildup　and　extinction　process　in　solid-state　lasers,　which　would　help　investigate　both　the　evolution　of　mode　locking　and　characteristics　determination　for　solid-state　lasers.