Transmission-type single-walled carbon nanotube saturable absorbers were successfully fabricated and used in a CW passively mode-locked Yb:Y₂SiO₅ laser for the first time to our knowledge. We obtained pulses as short as 1.1 ps around a center wavelength of 1058 nm. The average output power of 1.1 W was achieved at the repetition of 96.7 MHz; the corresponding peak power and energy of a single pulse was 10.3 kW and 11.4 nJ, respectively.