In the present paper, we discuss the design of a projection system with curved display and its enhancement by variably adjusting the curvature. We demonstrate that the focal surface curvature varies significantly with a change of the object position and that it can easily be computed with the Seidel aberration theory. Using this analytically derived curvature value as the starting point, we optimise a refocusable projection system with 90 degress field of view and F/# = 6.2. It is demonstrated that such a system can provide stable image quality and illumination when refocusing from infinity to 1.5 m. The gain in spatial resolution is as high as 1.54 times with respect to a flat focal surface. Furthermore, we prove that a silicon die can be curved to the required shape with a safety factor of 4.3 in terms of the mechanical stress. Finally, it is shown that the developed system can be used in a virtual reality headset providing high resolution, low distortion and a flexible focusing mode.