A rectangular filtering dielectric resonator antenna (FDRA) with low profile, wide bandwidth, and high gain is first investigated in this communication. It is fed by a microstrip-coupled slot from bottom, with open stub of the microstrip feedline elaborately designed to provide two radiation nulls at band edges for a filtering function. A separation is introduced in the slot to provide a good suppression level in lower stopband, while two parasitic strips are parallelly added to the microstrip feedline to offer good suppression in the upper stopband, and consequently, a compact FDRA with a quasi-elliptic bandpass response is obtained without involving specific filtering circuits. Based on the design, a modified DRA fed by a pair of separated slots is proposed to further enhance the gain by ~4 dB. A prototype operating at 5 GHz has been fabricated and measured for demonstration. The reflection coefficient, the radiation pattern, and the antenna gain are studied, and reasonable agreement between the measured and simulated results is observed. The prototype has a 10-dB impedance bandwidth of 20.3%, an average gain of 9.05 dBi within passband, and an out-of-band suppression level of more than 25 dB within a wide stopband.