In this paper, effects of frequency dispersive dielectric properties of a half-spherical breast phantom model on breast cancer tumor detection capability of the microwave radar-based imaging system, currently being developed at the Scientific and Technological Research Council-BILGEM-UEKAE, are investigated by simulation studies. An ultra wideband (UWB) bow-tie antenna array surrounding the breast has been designed in the presence of the breast phantom. The designed antenna operates efficiently across the band from 1 GHz to 8 GHz and it's assumed to be immersed in a coupling medium to get a good impedance matching with the breast. Fidelity factor of the case with the dispersive breast phantom is found to be 4.14% less than the non-dispersive case, due to increasing pulse distortion in dispersive dielectric tissues. Images are formed by using delay-and-sum (DAS) algorithm for the detection of spherical tumor with 2 mm diameter. Imaging results of the case with the dispersive breast phantom present signal reduction of 0.628 dB in the tumor response level as well as faulty locating of the tumor in the image, as compared to the successful results of the non-dispersive case. A better imaging algorithm compensating the dispersive effects will be used in the future.