The magnetic field of red giants is still poorly understood today. Close to the core, asteroseismology has revealed magnetic fields of several hundred thousand gauss, but close to the surface, spectropolarimetric observations of the red giant Pollux only showed an average field of the order of 1 G. Using the ASH code, we conduct a series of 3D nonlinear magnetohydrodynamical simulations aiming at modeling the dynamo process operating within the extended convective envelope of a star similar to the red giant Pollux. We find that the dynamo is efficient even for the slow rotation considered and that large-scale fields are generated and maintained. We further test the correlation between the scale of the convective motions and the surface magnetic field geometry by varying the Prandtl number in our simulations. We show in particular that the value and the geometry of the modeled surface field depend directly on the coupling scales between the magnetic and the velocity fields, with larger convective cells leading to a stronger large-scale magnetic field. We also verify that the dynamo and the geometry of the resulting field are robust against a change of the initial conditions. We then compare our simulations to the observed field and find average ∣B$_{ℓ}$∣ of about 7 G for the simulation with large convective cells, and down to 2 G for the smaller-scale simulation, very close to the observed value. Finally, we suggest the possibility of the reversal of the red giant’s magnetic field.