STORY: Inspectors from the U.N. International Atomic Energy Agency team, led by Grossi, braved intense shelling to reach the site on Thursday.
Grossi, after returning to Ukrainian-held territory, said he expects to produce a report early next week, and two IAEA experts would stay on at the plant for the longer term.
The site sits on the south bank of a huge reservoir on the Dnipro River, 10 km (6 miles) across the water from Ukrainian positions.
Both sides have accused the other of shelling near the facility which is still operated by Ukrainian staff and supplies more than a fifth of Ukraine's electricity in peacetime.
Kyiv also accuses Russia of using it to shield its weapons, which Moscow denies. Russia has so far resisted international calls to pull troops out of the plant and demilitarize the area.