A filtering dielectric resonator (DR) antenna (DRA) that does not require any filtering circuits is investigated. It deploys a rectangular DR and three slots fabricated in the ground plane. The antenna is excited in the fundamental TE <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1δ1</sub> DRA mode and two slot modes. By making use of these three modes, two tunable radiation nulls near the edges of the passband can be obtained, giving filtering effects without the need for any filtering circuits. In this article, the design, with minor modifications of the slots, is extended to a frequency-reconfigurable filtering DRA by using varactors. Its stopband can be extended to the third harmonic. By varying the voltages of the varactors, the antenna has continuous frequency agility of 27.7% (2.15-2.84 GHz), with almost the same harmonics suppression level. The antenna has a gain of ~5.0 dBi and a rejection level of over 16.1 dB across the stopband. Its total antenna efficiency in the passband is ~81%, whereas it is generally lower than the average value of 1.8% in the stopband (up to 7.0 GHz). Compared with the reported frequency-reconfigurable filtering antennas, our design has better frequency agility, more stable filtering response, and weaker radiation in the stopband.