This article borrows some or all of it's text from this article at Wikipedia.
In 1992, Torvalds explained how he pronounces the word Linux:
'li' is pronounced with a short [ee] sound: compare prInt, mInImal etc. 'nux' is also short, non-diphtong, like in pUt. It's partly due to minix: linux was just my working name for the thing, and as I wrote it to replace minix on my system, the result is what it is... linus' minix became linux.
—Linus Torvalds, comp.os.linux newsgroup, "Re: How to prounounce Linux?"
Torvalds has made available an audio sample which indicates his own
pronunciation, in English and Swedish. However, an interview from the
2001 documentary Revolution OS indicates that his preferred
pronunciation has slightly changed.
Many English speakers tend to pronounce the name as /ˈlɪnʊks/, lin-uks.