Unfortunately, almost no composite bows have survived from antiquity.  The Greeks in general were supposed to use bows made from horn, perhaps the horns of the ibex.  A modern reproduction of such a weapon is shown in one of the Primitive Bowyer's Bible series.   
The Wiki article speculates that the Cretans used bows made likewise, a composite bow made of horn glued up over a wooden center section.

This would be very similar to what would become pretty much standard as East Asian composite/recurve bows as used by the Turks, Mongols, and various other later peoples.