This paper presents a wideband or dual-band circular disk antenna with high gain and sidelobe suppression (SLS). The antenna has a single layer and single-fed configuration. The antenna can operate with the radiation field superposition of TM12 and TM14 modes at one frequency, which provides high gain and SLS. A circle of 10 shorting vias with non-identical diameters are loaded inside the antenna cavity in order to excite the field superposition of TM11 and TM13 modes at another frequency. By modifying the radius of the vias, the resonant frequency with the TM11 and TM13 superposition can be tuned closer to or further away from the one with the TM12 and TM14 superposition. In this way, a wideband or dual-band behavior can be obtained with high gain and SLS. The proposed antenna achieves the impedance bandwidth of 6.46% for the wideband case, which is over 6 times wider than the previous literature. In the dual-band case, the bandwidth is 1.48% and 1.61% at each band. For both cases, the gain and the SLS are higher than 15 dBi and 10dB within the operating bands, respectively. Measurements are carried out with prototypes and agree well with simulations.