The　continuous-wave　single-frequency　single-end-pumped　Yb:GdCOB　crystal　laser　is　designed　and　experimentally　demonstrated.　A　novel　output　method　is　proposed　to　achieve　the　spatial　and　fiber　output　with　compact　sandwiched　structure,　and　the　single-frequency　operation　is　realized　in　an　ultrashort　cavity.　The　maximum　output　power　is　40.9　mW　and　the　slope　efficiency　is　13.7%　at　1083.2　nm　with　360　mW　incident　power　and　a　1-mm-thick　crystal,　and　the　fiber　output　power　is　337　μ　W.　Meanwhile,　the　maximum　single-frequency　output　power　is　4.5　mW　at　1078.2　nm　with　380　mW　incident　power　and　a　0.2-mm-thick　crystal.