An electronic device may be provided with a display. The display may be formed from an array of organic light-emitting diode display pixels. Each display pixel may have an organic light-emitting diode having an anode and a cathode and may have an associated pixel circuit for controlling the light-emitting diode. The anodes may be formed from patches of metal arranged in an array on the display. The display pixels may be controlled using data lines and gate lines. The gate lines may control thin-film transistors in the pixel circuits. Gate driver circuitry along the left and right edges of the display may supply signals to the gate lines. The pixel circuits may be located in the center of the display between the gate driver circuitry. Some of the anodes may overlap the pixel circuits and some of the anodes may overlap the gate driver circuitry.