An anti-CD4 antibody which binds to CD4, has a high affinity and has a high effector activity, such as an antibody-dependent cellular cytotoxicity (ADCC activity) or complement-dependent cellular cytotoxicity (CDC activity), is required for a disease relating to a CD4-expressing cell.The present invention can provide a monoclonal antibody or an antibody fragment thereof, which binds to a CD4 extracellular region with high affinity and also exhibits a high ADCC activity or a high CDC activity; a hybridoma which produces the antibody; a DNA which encodes the antibody; a vector which contains the DNA; a transformant obtainable by introducing the vector; a process for producing an antibody or an antibody fragment thereof using the hybridoma or the transformant; and a therapeutic agent using the antibody or the antibody fragment thereof or a diagnostic agent using the antibody or the antibody fragment thereof.