Mark Haysom, who led the organisation for more than five years, said he wanted to take personal responsibility for problems with the colleges rebuilding programme.
Last week the government confirmed that building projects worth £3bn at 79 colleges have been put on hold because the LSC mismanaged the programme.
The LSC should never have given the projects the go-ahead, because of a shortfall in government funding. But many of the colleges have already started the projects, so risk losing money by suspending the work.
Haysom said: "No matter where those mistakes have been made and no matter how many people have been involved in the capital programme, as the chief executive of the LSC I am, of course, finally accountable. That is why I have made my decision to step down."
The LSC also came under fire last year for failing to provide students with Education Maintenance Allowance payments on time.
Haysom's salary was £207,838. He will be paid six months' notice, in line with his contract of employment. But he will not receive any bonus payment in relation to performance in the year up to March 2009.
Geoffrey Russell, who previously advised the government on financial matters at accounting firm KPMG, has been appointed as acting chief executive of the LSC.
The LSC will be dissolved by April 2010, when it will be replaced by the Skills Funding Agency and the Young People's Learning Agency.
Ministers have appointed the former head of the Audit Commission, Sir Andrew Foster, to prepare a report into the failings at the LSC.
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