Described herein is the identification of human monoclonal antibodies that bind GPC3 or heparan sulfate (HS) chains on GPC3 with high affinity. The antibodies described herein are capable of inhibiting HCC cell growth and migration. Provided are human monoclonal antibodies specific for GPC3 or HS chains on GPC3, including immunoglobulin molecules, such as IgG antibodies, as well as antibody fragments, such as single-domain VH antibodies or single chain variable fragments (scFv). Further provided are compositions including the antibodies that bind GPC3 or HS chains on GPC3, nucleic acid molecules encoding these antibodies, expression vectors comprising the nucleic acids, and isolated host cells that express the nucleic acids. Methods of treating cancer and/or inhibiting tumor growth or metastasis are also provided. Further provided are methods of detecting cancer in a subject and confirming a diagnosis of cancer in a subject.