The two-seater Cessna 152 flew between the parachutists' canopies over Cambridgeshire, the UK Airprox Board (UKAB) said.
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The pilot was "already among the parachutists" by the time he spotted them and turned his aircraft to the right to avoid contact, the report stated.
It had "simply been providence that had prevented a collision", according to the UKAB, who deemed the degree of risk to be in the most serious category.
Just 300ft separated the plane from the canopies, the pilot of the aircraft which dropped the parachutists estimated.
The near-miss occurred at an altitude of around 2,000ft in the parachute drop zone above Chatteris aerodrome, north Cambridgeshire, on May 15.
The Cessna pilot "acknowledges that he misappreciated his position" and "understands the execution of this flight was not perfect", the UKAB said.