A display may have an array of organic light-emitting diode display pixels. Each display pixel may have a light-emitting diode that emits light under control of a drive transistor. Each display pixel may also have control transistors for compensating and programming operations. The array of display pixels may have rows and columns. Row lines may be used to apply row control signals to rows of the display pixels. Column lines (data lines) may be used to apply display data and other signals to respective columns of display pixels. A bottom conductive shielding structure may be formed below each drive transistor. The bottom conductive shielding structure may serve to shield the drive transistor from any electric field generated from the adjacent row and column lines. The bottom conductive shielding structure may be electrically floating or coupled to a power supply line.