Humans are classified as vertebrate which means that they have a true skeleton and a backbone. However some animals in other phylum seem to possess that characteristic though not really to the full extent. Insects, mollusks and echinoderms are all invertebrates.  Among the invertebrate, the closest phylum are the echinoderms. Here are some reasons why echinoderms are the closest animal related to humans:

During at larval stage, echinoderms have notochord which apparently disappears as they grow to a mature animal. They also have throat openings (pharyngeal gill slits); nerve cells; and a muscular tail that extends past the anus. 

Recently, genomic sequences have shown that sea urchins (an echinoderm) prose many similarities with vertebrates.