The present invention relates to an anti-CD19 antibody having a variant Fc region having some specific amino acid modifications relative to a wild-type Fc region which confer one or several useful effector functions. The present invention relates in particular to chimeric, humanized or full human anti-CD19 antibodies comprising such a variant Fc region. It relates advantageously to antibodies with an interesting and valuable glycosylation profile, especially a low fucose level and/or a high oligomannose level and low level of sialic acid, high ADCC function and no CDC. The present invention also relates to the use of these antibodies in the treatment, prevention or management of diseases or disorders, such as cancer, especially a B-cell malignancy and auto-immune disease.