An electronic device may be provided with wireless circuitry that includes a phased antenna array. The array may include first, second, and third rings of antennas on a dielectric substrate that cover respective first, second, and third communications bands greater than 10 GHz. The second ring of antennas may surround the first ring of antennas. The third ring of antennas may be formed over the second ring of antennas. Parasitic elements may be formed over the first ring of antennas to broaden the bandwidth of the first ring of antennas. Beam steering circuitry may be coupled to the rings of antennas. Control circuitry may control the beam steering circuitry to steer a beam of wireless signals in one or more of the first, second, and third communications bands. The array may exhibit relatively uniform antenna gain regardless of the direction in which the beam is steered.