Yb-doped YCa₄O(BO₃)₃ or YCOB is an acentric crystal interesting for ultrashort pulse generation and self-frequency doubling lasers. Femtosecond mode-locking was investigated for Yb:YCOB in a standard Z-cavity. The pump laser was a two-section distributed Bragg-reflector tapered diode-laser at 976 nm. Mode-locking using a SESAM was achieved for all the three polarization orientations of Yb:YCOB. The shortest pulse duration of 69 fs with an average output power of 58 mW were obtained directly from the oscillator with a Y-cut Yb:YCOB sample for the E//Z polarization. The output spectral bandwidth was 26.7 nm (FWHM) centered at 1050 nm, corresponding to a time-bandwidth product of 0.49. After the additional external compression performed by the use of a sequence of chirped mirrors, pulse durations as short as 49 fs were achieved, and the corresponding time-bandwidth product of 0.36 was already close to the Fourier limit. The achieved pulse durations with Yb:YCOB are among the shortest pulses demonstrated with mode-locked Yb lasers. Shorter pulses with a duration of 47 fs have been reported only once before, with Yb:CaGdAlO₄ [Y. Zaouter et al., Opt. Lett. 31 (2006) 119].