Dear Friends, The Minoan civilization was among the earliest on Greek islands. Did the Island of Crete have its own version of Greek language and what was the dialect called ? Or which Greek could it be closest to ?
sinhakumara. 
It depends what period of history you’re talking about. The island of Crete was settled by Greeks during the Mycenean period. Evidence suggests that they brought their language with them.
However, I assume you mean the earlier civilization that created the Minoan palaces. The short answer: we don’t know what language they spoke.
Have you tried doing a google search on this? The keywords “Linear A” and “Linear B” should help you get started.
Also there’s a small, fascinating book by Chadwick (?) “The Decipherment of Linear B” that is very good about the discovery that Linear B is actually early Greek (Bronze Age). Apparently this was the language used in Mycenean Greece and Minoan Crete, and if so, the Mycenaeans and the Minoans could have understood each other. Minoan Crete is definetly one of THE topics to get into-wish I knew more about it. Paige.
My understanding was that Linear B dates from a time when Crete had already been settled (taken over) by Mycenean Greeks. If so, it is an indication that the Greeks brought their language with them, but not that the language of the previous inhabitants was also Greek. Linear A seems not to have been Greek; Linear B was an adaptation of this script to Greek phonology.
A very poor adaptation from what I’ve seen 
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You guys may be right-my impression was that inscriptions in Linear B have been found in Crete that pre-date the Mycenaeans, which would mean it was the common language. Next time we get snowed in here, I 'm going to get out all the stuff I have about Minoan civ. and try to absorb it all.
There’s also the Eteocretans (the “true” Cretans) who left behind inscriptions in a non-Greek language. I believe that most scholars think they’re the descendants of the Minoans.