A fast responsive two-dimensional/three-dimensional (2D/3D) switchable display is demonstrated based on an active liquid crystal (LC) microlens array and a twisted nematic (TN) cell. Compared with the traditional LC microlens array, the fabricated LC microlens array has more ideal phase profile and better focusing effect. The TN cell can switch the polarization direction of the incident light with a very short switching time (4.3 ms) and a small driving voltage (5Vrms). By introducing the tilted elemental image arrays and tilted LC lens array, the moiré patterns are eliminated. The fast switching of the 2D/3D display can be realized by applying or removing voltage to the TN cell. The fast responsive 2D/3D switchable display with the LC microlens array and the TN cell is thin and compact without moiré pattern compared with other 2D/3D switchable display devices.