The present invention provides an active matrix substrate and an organic EL display device in which reduction in the response rate of a current-driven light-emitting element is suppressed. The active matrix substrate of the present invention is an analog gradation-driving active matrix substrate, including multiple pixels each including a current-driven light-emitting element and a drive transistor. The current-driven light-emitting element includes a pixel electrode electrically coupled with the drive transistor. The drive transistor supplies a current to the current-driven light-emitting element through the pixel electrode. The multiple pixels include a first pixel and a second pixel disposed adjacent to each other. A gate electrode of the drive transistor of the first pixel is disposed between the pixel electrode of the current-driven light-emitting element of the first pixel and the pixel electrode of the current-driven light-emitting element of the second pixel in a plan view of a main face of the substrate.