The present invention provides CTLA-4 monoclonal antibodies, particularly humanized monoclonal antibodies specifically binding to CTLA-4 with high affinity. The present invention also provides functional monoclonal antibodies cross-reactive to CTLA-4 of human, cynomolgus monkey and mouse. The present invention further provides amino acid sequences of the antibodies of the invention, cloning or expression vectors, host cells and methods for expressing or isolating the antibodies. The epitopes of the antibodies are identified. Therapeutic compositions comprising the antibodies of the invention are also provided. The invention also provides methods for treating cancers and other diseases with anti-CTLA-4 antibodies.