We report on the first sub-60 fs pulse generated from a diode-pumped SESAM mode-locked Yb-laser based on a non-centrosymmetric Yb:YAl3(BO3)4 crystal as a gain medium. In the continuous-wave regime, pumping with a spatially single-mode, fiber-coupled 976 nm InGaAs laser diode, the Yb:YAl3(BO3)4 laser generated 391 mW at 1041.7 nm with a slope efficiency as high as 65.1%, and a wavelength tuning across 59 nm (1019 to 1078 nm) was achieved. By implementing a commercial SESAM to initiate and sustain the soliton type mode-locking, and using only a 1 mm-thick laser crystal, the Yb:YAl3(BO3)4 laser delivered pulses as short as 56 fs at a central wavelength of 1044.6 nm with an average output power of 76 mW at a pulse repetition rate of ∼67.55 MHz. To the best of our knowledge, this result represents the shortest pulses ever achieved from Yb:YAB crystal.