Minoan's board said that "following a review of the group's businesses and acquisition strategies" it had decided to "buy in" the stake for £160,000 more than it sold it for.
"The board believes that the acquisition (which is expected to be earnings enhancing) is in shareholders' best interests in that it will enable the group to pursue a more flexible approach to the acquisition strategy for its T&L business," Minoan said.
Minoan is paying £930,000 for the 20% stake after having sold it for £770,000 on July 31.
Minoan, which has never named the investor, said the difference in the price reflected the growth of the business.
The original agreement included a "buy back" arrangement which could have amounted to up to £1.1 million, Minoan said.
The deal comes after Alternative Investment Market-listed Minoan managed to secure a £5m loan facility from Jersey-based family office Hillside International Holdings in October.
The company announced yesterday that it had secured a further deal with lenders to revise the terms of their loan agreements.
This has made sure that some £1.2m of its debts can be repayable at the lenders' discretion, either in cash or in shares at a price of 8.5p per share.
This means that Minoan could issue up to another 14.25m shares before the end of October 2016.
Its deal with Hillside includes warrants that allow that company to subscribe for up to 50m Minoan shares at 8p a share over the next four years.
Minoan's shares finished the day's trading down 0.375p, or 3.7%, at 9.75p.
This compares to a 52-week high of 11.75p reached on December 31 although the shares were trading as low as 4p last summer.
Led by Duncan Wilson, who ran the Direct Holidays business built by John and Hugh Boyle, Minoan has bought several businesses in Scotland under a plan to consolidate small travel operators.
Minoan told investors yesterday that gross revenues for the year to the end of October are likely to come in at £50m, some £5m more than its previous guidance provided last month.
It continued to guide that operating profits would come in at more than £600,000 for the year.
Minoan also reported that its partnership with Candia Investment Corporation, first announced in the summer of 2012, has resulted in a £1m investment handing the Monaco administered fund a 5% interest in its site in north Crete.
Candia had pledged to acquire a stake of up to 10% in the project for £2m payable in tranches. Minoan said that it has now been agreed "that the remaining tranche of £1m will become due at such time as the parties determine".
The project has faced delays due to the political uncertainty in Greece.
Christopher Egleton, chairman of Minoan, whose businesses include Ski Travel Centre, Stewart Travel, John Semple Travel and King World Travel, said: "I am very pleased that we have been able to complete the buy in of the 20% stake in our T&L business from existing resources and hope to update shareholders with further positive developments for the group's business in both Greece and the UK in the very near future."
Last month Minoan's directors opted to take some of their pay in shares and share options to bolster its working capital and encourage potential investors.