over the next 10 days, to mark its 10th year of operation.
To enter, people have to -- an algorithm will randomly choose a winner.
The first computer has just been given away to a London-based twitterer, , and now thousands more are tweeting the required term in a bid to win the next one.
People are invited to tweet the term as many times as possible, leading to #moonfruit becoming a trending topic.
These appear on the front of the Twitter site and encourage thousands more users to click and see what it is that everyone is talking about on the site.
Moonfruit makes software that lets people build websites without having any design or web building experience.
Joe White, managing director, Moonfruit, said: "We've been overwhelmed by the response to the campaign which has reached 2.5% of all twitter traffic at the time of the 2nd winner. And we love how people are playing with the Moonfruit name and being really creative and funny. We're glad people are treating this with a sense of humour. It is our birthday after all."
In January this year, Lenovo (the brand formerly known as IBM) used Twitter to run a discount promotion giving people as much as £200 off a new laptop.