A global electromagnetic gyrofluid model based on the full-F gyrokinetic model is derived. The gyrofluid moment variables are not split into fluctuating and equilibrium parts. Profiles are evolved freely, and gyro-averaging operators are not parametrized, but are functions of the gyrofluid moment variables. The fluid moment hierarchy is closed by approximating the gyrokinetic distribution function as a finite order Hermite-Laguerre polynomial and by determining closure approximations for terms involving the gyrokinetic gyro-averaging operator. The model exactly conserves the gyrokinetic full-F energy invariant evaluated using the Hermite-Laguerre decomposition. The model is suited for qualitative studies of the interplay between turbulence, flows, and dynamically evolving profiles in magnetically confined plasmas.