Blue phases are types of liquid crystal phases that appear in a temperature range between a chiral nematic phase and an isotropic liquid phase. Because blue phases have a three-dimensional cubic structure with lattice periods of several hundred nanometres, they exhibit selective Bragg reflections in the range of visible light corresponding to the cubic lattice. From the viewpoint of applications, although blue phases are of interest for fast light modulators or tunable photonic crystals, the very narrow temperature range, usually less than a few kelvin, within which blue phases exist has always been a problem. Here we show the stabilization of blue phases over a temperature range of more than 60 K including room temperature (260-326 K). Furthermore, we demonstrate an electro-optical switching with a response time of the order of 10-4 s for the stabilized blue phases at room temperature.