The radio frequency (RF) negative hydrogen ion source is employed in neutral beam injection (NBI) system for magnetic confined fusion devices. To satisfy the required beam current of negative hydrogen ions in NBI for fusion, the surface production on the plasma grid (PG) surface is introduced to increase the amount of negative hydrogen ions. In this paper, a 2D fluid model is established, including volume production and surface production of negative hydrogen ions. This work focuses on the spatial distributions of negative hydrogen ions with different gas pressures, PG bias potentials, magnetic filter filed (MFF) positions and RF powers. The results show that the density of negative hydrogen ions is enhanced by the surface production. As the gas pressure increases, the increase in the negative hydrogen ion density is dominated by the increase in the conversion of neutral hydrogen atoms at the PG surface. As the bias potential increases, the distribution of negative hydrogen ions is slightly shifted towards the PG due to the reduction of electric field near the PG. As the MFF position shifts towards the PG, the increase in the negative hydrogen ion density is dominated by the increase in the conversion of positive hydrogen ions at the PG surface. Moreover, the negative hydrogen ion density increases with the increased RF power, which is dominated by the increase in the conversion of positive hydrogen ions at the PG surface. The model facilitates the understanding of the negative hydrogen ion distribution and the optimization of negative hydrogen ion production.