We report superconductivity at T(c) ≈ 2.6 K in a new layered bismuth oxyselenide LaO(0.5)F(0.5)BiSe2 with the ZrCuSiAs-type structure composed of alternating superconducting BiSe2 and blocking LaO layers. The superconducting properties of LaO(0.5)F(0.5)BiSe2 were investigated by means of dc magnetization, resistivity and muon-spin rotation experiments, revealing the appearance of bulk superconductivity with a rather large superconducting volume fraction of ≈ 70% at 1.8 K.