We report on mode-locking of an Yb:Ca3NbGa3Si2O14 laser, which is pumped by a fiber-coupled single-mode laser diode. The shortest pulse duration obtained with a semiconductor saturable absorber mirror is 52 fs, with 75 mW of average output power. Sub-60 fs operation tunable between 1055 and 1074 nm is achieved by employing semiconductor absorbers with different characteristics. We also demonstrate passive mode-locking results with transmissive graphene saturable absorber, reaching an 85 fs pulse duration with 23 mW output power. Moreover, we present the non-phase-matched self-frequency doubling properties of this non-centrosymmetric crystal in the femtosecond regime.