Paleolithic diet food list. Foods perfect for caveman Paleolithic diet recipes. The Paleolithic diet menu consists of meals of fish, meat, nuts, roots, vegetables, and fruits. The diet plan avoids dairy, salt, refined sugar, legumes, and grains. This special diet is based on the supposed ancestral diet dating back to the Paleolithic era. Proponents of this diet argue that those who follow it are largely disease free. However, criticism of this diet labels it a fad and even extreme in its logic. However, if you want to experience how life could've been like for a hunter-gatherer (at least in culinary terms), you may want to try this diet--even if it's just for a week or two.