The invention relates to recombinant antibodies which bind to prostate-specific stem cell antigen (PSCA). The antibody of the invention comprises complementarity-determining regions (CDR) having the following amino acid sequences: CDR of the variable region of the light chain: CDR1 SEQ ID No. 1, CDR2 SEQ ID No. 2, CDR3 SEQ ID No. 3, and CDR of the variable region of the heavy chain: CDR1 SEQ ID No. 4, CDR2 SEQ ID No. 5, CDR3 SEQ ID No. 6. The invention also embraces the use of the antibodies of the invention as medicinal products, especially for the treatment of tumor diseases, or as a diagnostic agent. The antibodies are suitable for use in the areas of medicine, pharmacy and biomedical research.