Davide Cocco Palmieri was an Italian, Roman Catholic prelate who served as the Bishop of Malta from 1684 until 1711.

He was ordained priest of the Sovereign Military Order of Malta on February 24, 1657.

Two years after Bishop Molina was transferred to another diocese in Spain, Pope Innocent XI appointed Cocco Palmieri as his successor on May 15, 1684.

Cocco Palmieri was greatly esteemed by Grand Master Alof de Wignacourt.

During his bishopric Cocco Palmieri opposed the privileges that of the Roman Inquisition.