The influence of cross-sectional geometry on critical current in thin superconducting tape at self-field and external applied field is investigated based on the field-dependent critical state model. The critical current density profiles in the curved tape, V-shape tape, and U-shape tape exhibit quite different features from the flat tape. At self-field and external applied field, it is found that different cross-sectional geometries can lead to an enhancement or a reduction of critical current Ic, as compared with that for a flat tape, depending on the amplitude of applied field. The results of this paper are useful to optimize the cross section of superconducting tape for achieving high critical current.