A sun-shade assembly includes a stationary curved shaft, a tubular roller, a screen, and a torsion spring. The roller is made of a resilient material, and is sleeved rotatably around the shaft. The roller has a curvature conforming with that of the shaft. The screen is wound around the roller, and has a lower edge connected to the roller and an upper edge provided with a stretch rod which has a curvature conforming with that of the shaft. The torsion spring has a first end secured to the roller, and an opposite second end secured to the shaft. The screen is unwound from the roller when the stretch rod is pulled away from the roller, thereby resulting in rotation of the roller about the shaft in a first direction against biasing force of the torsion spring. The torsion spring biases the roller to rotate about the shaft in a second direction opposite to the first direction to result in winding of the screen onto the roller.