A dual-band antenna with little limitation on the mounting space, which allows two antenna elements coping with different frequency bands to be laid out at a narrow space, and a portable wireless device having the same are provided. A band-like first antenna element, a sheet-like dielectric element, and a band-like second antenna element are fitted in a groove of a support member. The end portion of the second antenna element overlaps with the end portion of the first antenna element, and the dielectric element is sandwiched therebetween. The sandwiched dielectric element constitutes a capacitor, and first antenna element, the capacitor and the second antenna element are connected in series. The other end portion of the second antenna element is connected to a circuit in a bottom casing, and power is supplied through the other end portion thereof.