An ultra-wideband (UWB) rectangular dielectric resonator antenna (DRA) integrated with a narrow-band (NB) DRA is presented. The proposed antenna consists of a UWB DRA excited by a planar monopole and a DRA excited by a slot which displays NB characteristic. The UWB and NB antenna provides a 2:1 voltage standing wave ratio (VSWR) bandwidth for 2.5 -11 GHz and 5.1 -5.5 GHz, respectively, with the same polarization and a reasonable isolation (better than -10 dB ) between the two ports. Moreover, the NB antenna can operate in 6.8 -7.3 GHz or 3.75 -3.88 GHz by little modification. This is a promising candidate for applications of cognitive radio, where a UWB antenna is for spectrum sensing and a NB antenna for communication operation. To improve the isolation between the two ports, several arrangements are investigated.