We demonstrate a diode-pumped femtosecond Yb:CaGdAlO4 (Yb:CALGO) laser with a semiconductor saturable absorber mirror (SESAM) for stable mode-locking operation. A perfect beam profile is measured under 10 W output power with $M_{x}^{2}$ = 1.017 and $M_{y}^{2}$ = 1.016 in the horizontal and vertical directions, respectively. At the repetition rate of 71.66 MHz, the optical pulse duration is 247 fs and the pulse energy is 140 nJ at the central wavelength of 1041 nm, corresponding to a peak power of 0.56 MW. In addition, we also generate continuous wave (CW) power of more than 15 W with TEM00 mode, corresponding to an optical-to-optical efficiency of 44.1%.