Heathrow says the charges, which need to be approved by the Civil Aviation Authority (CAA), will help pay for £3 billion of investment, including the opening of the new Terminal 2 next year.
Airport bosses said that errors in previous passenger forecasts meant that Heathrow had lost out on around £650 million of charges over the last five years.
The CAA had based the previous level of charges on estimates that Heathrow would handle 78 million passengers a year by 2013, but the airport is only handling around 70 million.
If approved, Heathrow's charges will increase from the equivalent of £19.33 per passenger for 2012/13 to as much as £27.30 in 2018/19.
Year by year breakdown:
2012/2013 - £19.33 per passenger
2013/2014 - £20.78 per passenger
2014/15 - £21.96 per passenger
2015/16 - £23.25 per passenger
2016/17 - £24.50 per passenger
2017/18 - £25.81 per passenger
2018/19 - £27.30 per passenger
Passengers using Heathrow face a rise in ticket prices under a £3 billion investment plan proposed today by the airport's bosses.
If regulators approve the five-year plan, it would allow Heathrow to charge airlines higher fees.
That means an increase equivalent to more than £19 per passenger from the end of this year, rising to more than £27 in 2018.
Luton based airline easyJet is to create 330 new jobs for pilots this year across its 11 UK bases, which include Southend, Luton and Stansted.
The company says it offers a clear career path for pilots with the potential to move from first officer to captain more quickly than other airlines.
The head of British Airways' parent company, Willie Walsh, has warned that Heathrow will soon be overtaken by Dubai as the world's biggest international airport.
Speaking to the House of Commons Transport Committee, Mr Walsh said that the Middle Eastern airport had grown massively over the last decade - and could outstrip Heathrow "within two to three years".
In 2001, Dubai was the 99th biggest international airport in the world. By 2001 it was in 13th position and by 2011 it was fourth, he said.
A report out today by Heathrow Airport is calling for a London "hub" airport. Interestingly this doesn't stress the need for a third runway. Is it that investors are not keen on risk?
Heathrow Airport chief executive Colin Matthews says: "We say a hub (airport) matters but actually does it matter to the country as a whole?
"The economic analysis we published today suggests it really does."
A lack of space to land planes at Heathrow airport is costing the UK up to 14 billion pounds a year in lost trade. A new report says the figure could rise. Bosses at the airport have been pushing for a third runway but government officials have ruled it out for the time being.