Thermal　rollover　is　one　of　the　fundamental　limitations　that　affect　the　output　power　and　modulation　bandwidth　of　high-speed　laser　in　monolithic　laser　integrated　circuits　(ICs).　Herein,　an　850　nm　vertical　cavity　surface　emitting　laser　(VCSEL)　with　p-doping　and　sub　quantum　well　(sub　QW)　centers　active　layer　is　proposed　and　investigated.　The　p-doping　and　sub　QW　insert　in　the　offset　position　of　each　barrier,　which　are　designed　for　reducing　the　thermal　rollover　and　increasing　the　maximum　intrinsic　modulation　bandwidth　of　the　laser.　Numerical　simulations　show　that　adding　the　p-doping　and　sub　QW　in　active　region　could　reduce　the　threshold　currents　(Ith),　improve　the　slope　efficiency　(SE)　and　delay　the　thermal　rollover　in　VCSEL.　Comparing　with　previous　VCSEL,　our　proposed　VCSEL　has　excellent　high　temperature　output　performance,　and　the　maximum　simulation　3-dB　bandwidth　is　43.9　GHz　at　25　degrees　C　and　33.1　GHz　at　85　degrees　C,　respectively.　Furthermore,　temperature-dependent　time-resolved　photoluminescence　(PL)　and　PL　excitation　reveal　this　novel　QW　has　strong　radiative　recombination　rate,　which　is　suitable　for　designing　active　region　of　high-speed　and　high　power　lasers.