Chief executive Geoff Webb said it was time to solve the problem after Tottenham Hotspur manager Harry Redknapp joined the long list of managers to criticise the pitch after his team's 2-0 defeat to Portsmouth in the FA Cup semi-final last weekend.
Webb said: "It's in everybody's interest (to solve the problem) because after 10 surfaces in three-and-a-half years, members of the public start to look at it and ask questions. We would suggest that an independent enquiry would be in the best interests of everyone to understand the nature and cause of the ongoing issues concerning Wembley's playing surface.
"The IoG would be a willing partner in facilitating a possible solution. We would welcome the opportunity to lend our expertise to solve the problem."
He said the industry suffers every time a match is played at the national stadium as the constant scrutiny means the first thing criticised is the standard of grounds management.
It is almost 12 months since previous grounds manager Steve Welch was replaced and the Sports Turf Research Institute (STRI) was brought in to consult. But the STRI is fighting against a hectic schedule of fixtures and events with which the stadium was not designed to cope.
Webb added: "Since the problems still persist with the playing surface, the IoG believes it is time to bring the experts together who can independently offer solutions.
"Many Premier League stadia serve as excellent examples of football surfaces. Their playing surfaces are clearly sacrosanct and non-football events are limited. Surfaces are not replaced regularly - they are managed and maintained year-round to a very high level."