High-quality monolayer graphene as large as $1.2\times 1.2{\mathrm{cm}}^2$ was synthesized by chemical vapor deposition and used as a transmitting saturable absorber for efficient passive mode-locking of a femtosecond bulk solid-state laser. The monolayer graphene mode-locked Cr:forsterite laser was tunable around $1.25\mathrm{\mu m}$ and delivered sub- $100\mathrm{fs}$ pulses with output powers up to $230\mathrm{mW}$ . The nonlinear optical characteristics of the monolayer graphene saturable absorber and the mode-locked operation were then compared with the case of the bilayer graphene saturable absorber.