The potential distribution near the extraction region in negative ion sources for the plasma with the surface produced negative ions is studied analytically. The potential is derived analytically by using a plasma-sheath equation, where negative ions produced on the Plasma Grid (PG) surface are considered in addition to positive ions and electrons. A negative potential peak is formed in the sheath region near the PG surface for the case of strong surface production of negative ions or for low energy negative ions. Negative ions are reflected by the negative potential peak near the PG and returned to the PG surface. This reflection mechanism by the negative potential peak possibly becomes a factor in negative ion extraction. It is also indicated that the potential difference between the plasma region and the wall decreases by the surface produced negative ions. This also has the possibility to contribute to the negative ion extraction.