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He said he wanted to see a "fair taxation system" with corporations and the rich paying more.
Labour is also planning to link senior executives' pay to the average wage of the workers in the same company.
Mr McDonnell said a fair taxation system would see "the corporations and the rich pay their way more".
"That means ending the tax giveaways to the corporations and also those in inheritance tax, capital gains tax and the bankers' levy - all of those giveaways under this government," he told BBC Radio 4's Today programme.
"The rich will be above £70,000 to £80,000 a year - and that's roughly defined as what people feel is an earning whereby people feel they can pay more."
Mr McDonnell said middle and low earners were "being hit very hard" with a combination of income tax rises and "attempts by this government to increase National Insurance payments on the self-employed".
Less than a week after announcing them in last month's Budget, Chancellor Philip Hammond dropped plans to make self-employed people pay more National Insurance after they were criticised for breaking a 2015 manifesto pledge.
Mr McDonnell said Labour would go into the election promising to cap senior executives' pay with the introduction of "a pay ratio".
"That in itself will set a cap in terms of what the maximum earning will be within that company in relation to an average worker's pay, because we believe in fairness within our economy," he said.
Mr McDonnell said Theresa May's decision to seek an early election was more about the risk of an economic downturn than securing a mandate for her plans on leaving the European Union.
"I don't think this election is about Brexit," he said. "The government has seen that the economy at the moment is going to turn.
"We are seeing inflation increasing - we are seeing wages stagnate and we are seeing people in heavy debt as a result of that."
Labour's approach to Brexit talks would aim to secure "tariff-free access to the single market" and a managed and fair immigration system from the EU.
On future customs arrangements, Mr McDonnell said: "We want to maximise the benefits that we currently get from the customs union - that does not necessarily mean full membership of the customs union."