The Labour leader pledged to scrap hospital parking charges and cover the lost revenue with an 8% hike in insurance premium tax to 20% for private health insurance products.
The party estimates the tax rise will be enough to cover the Â£162 million that English hospitals raise annually from car parking charges.
It comes after shadow chancellor John McDonnell defended Labour's plans to put up taxes for those earning more than Â£80,000, while saying there was "a lot to learn" from Karl Marx's Das Kapital.
His comments were criticised by the Tories and Liberal Democrats and according to the Telegraph caused angst among some Labour figures.
Announcing Labour's free-parking plan while visiting nursing students in Tory-held Worcester, Mr Corbyn said: "Labour will end hospital parking charges, which place an unfair and unnecessary burden on families, patients and NHS staff.
"Hospital parking charges are a tax on serious illnesses.
"Our hospitals are struggling from under-funding at the hands of Theresa May's Conservative government, but the gap should not be filled by charging sick patients, anxious relatives and already hard-pressed NHS staff for an essential service.
"Our NHS needs a Labour government that will stand up for the many, not the few."
Labour's policy announcement follows a freedom of information request by the Unison union, which revealed that some hospitals are charging staff, including nurses, nearly Â£100 a month to park.
The tax hike on private healthcare insurance would raise an additional Â£377 million, the party estimated.
It would mainly hit corporate employers, who buy 80% of private medical insurance policies, often on behalf of wealthier high-skilled workers, Labour said, citing research from healthcare consultants LaingBuisson.
Unison general secretary Dave Prentis said: "The cost of hospital parking is heaping excessive financial pressure on health employees who've gone for years without a decent pay rise.
"Extortionate parking costs are bad enough, but NHS staff are also being hit with huge fines, or having to nip out every hour to feed the meter.
"A parking space at work isn't a luxury for those who work nights or in rural areas. Scrapping paid-for parking is the right thing to do for staff and patients alike."
A Conservative Party spokesman said: "This promise isn't worth the paper it's written on because Jeremy Corbyn simply wouldn't be able to deliver it.
"With Corbyn in charge of our Brexit negotiations, the economy and our NHS would be at grave risk.
"There would be less money to spend in hospitals, not more."