Sir David Higgins told MPs that it would be possible to have HS2 completed to Leeds and York by 2030 rather than the current projected 2033 date.
The move would not require extra finance but would need ministers to allow the existing budget to be spent more quickly.
Sir David said: “You can deliver stage 2b, that’s the section to Leeds, York, Manchester, by 2030 if you don’t put cash constraints on the delivery.
“So you can build it quicker there’s no doubt about that.”
He added: “Certainly it wouldbring the benefits further forward, it should do, it makes sense that it should, because if you can deliver it quicker you should be able to reduce the overheads costs.”
Sir David said the question for Government would be whether it made sense to spend more quickly on HS2 at the same time as it faced other demands including a major roadbuilding programme.
The HS2 chairman played down suggestions that the project could find itself competing for cash with proposals for the Crossrail 2 project in London.
But he admitted that Parliament could find it difficult to pass the legislation needed for both projects at the same time.
He also defended the major changes to HS2’s plans in South Yorkshire, announced earlier this year, that have seen proposals for a new station at Meadowhall scrapped.
HS2 will instead serve the existing Sheffield station via spur off the mainline at Chesterfield. The line will also now take a route much further east through South Yorkshire.
Sir David said the new proposal was £900m cheaper and would mean quicker journey times.
Lincoln MP Karl McCartney suggested the changes would mean some passengers would now have to travel north to Leeds to catch HS2 for journeys south.
Sir David said proposals for another “parkway” station in South Yorkshire would “open up to a lot of people who have no services whatsoever at the moment.
“And it’s extremely close to the A1/M1 which as time goes on is becoming a more and more critical corridor for access.”
He said Chesterfield would be a one hour journey from London.