We use a new (to our knowledge) fabrication method of a single-walled carbon nanotube (SWCNT) absorber without polymer to sustain high-power illumination. Using a series of saturable absorbers (SAs) incorporating different amounts of SWCNTs, we demonstrate mode-locking for a Nd:GdVO₄ laser in the 1 μm spectral range. Continuous-wave mode-locking (CWML) pulses with a maximum output power of 3.6 W at 1063 nm and high noise extinction of 61 dB has been achieved to give the highest pulse peak power of 3.6 kW and pulse energy of 30 nJ under 15 W pumping. To our knowledge, this is the highest CWML output power with SWCNT-SAs reported. The measured nonlinear absorption of the SWCNT-SAs shows a modulation depth of ~3% with subpicosecond recovery time.