A diode-pumped Yb:CLNGG laser is mode-locked with a single-walled carbon nanotube saturable absorber (SWCNT-SA) for the first time. Pulse durations as short as 90 fs are obtained at ~1049 nm with 0.4% output coupler, the shortest pulses to our knowledge for a diode-pumped 1-µm laser applying SWCNTs as saturable absorber. Using 3% output coupler, the maximum average output power reached 90 mW at a repetition frequency of 83 MHz.