The invention relates to a novel antibody and an antibody fragment thereof specifically binding to a B-cell maturation antigen (BCMA), and particularly relates to a fully humanized single-chain variable fragment (scFv). The invention further relates to a nucleic acid encoding the antibody, a vector, and a host cell expressing the nucleic acid. Furthermore, the invention also relates to a composition containing the antibody described herein, and use thereof in treatment and diagnosis.