Revenue and Customs is to recruit up to 1,000 extra staff to tackle delays in getting through to call centres.
The move is aimed at achieving a target of answering 90% of calls, two years earlier than planned.
Around £9 million of extra investment will be made this year, and up to £25 million in 2013-14 to reach the call centre industry standard by next spring.
Chief executive Lin Homer said money was being "reprioritised" to make the additional investment, without affecting other customer services.
HMRC has 17 contact centres across the UK, employing 8,500 staff, handling around 60 million calls a year.
Performance has improved from 48% of calls handled in 2010/11 to 74% in 2011/12, but HMRC said more needed to be done to provide a better service.
Ms Homer said: "It is vital that when customers call us for help their call is answered - and in a reasonable time. The feedback we get is that the quality of the advice we give when people get through is good, but we haven't been answering enough calls.
"Our target of achieving contact centre industry standards of 90% of calls answered first time is the right target. But after hearing the views of customers, stakeholder bodies and our own staff, we have speeded up our timetable for achieving it.
"I believe that we should be providing this important level of customer service sooner, not later, and investment of up to £34 million will enable us to do this by the end of March 2013 and sustain service levels during the next two years, rather than wait until 2015 to achieve the target. It will also enable us to reduce call waiting times drastically."
Exchequer Secretary David Gauke said: "Although there has been an improvement in contact centre performance over the last couple of years, too many callers have faced unacceptable delays in getting through. I welcome this announcement which should result in a much improved service."
Mark Serwotka, general secretary of the Public and Commercial Services union, said: "This is a positive step forward for HMRC and is something for which we have long argued.
"We would like to see this kind of recognition that investment is what our public services need, instead of more cuts, extended wider across the department and the civil service."