We investigate the properties of quantum radiation produced by a uniformly accelerating charged particle undergoing thermal random motions, which originates from the coupling to the vacuum fluctuations of the electromagnetic field. Because the thermal random motions are regarded to result from the Unruh effect, this quantum radiation is termed Unruh radiation. The energy flux of Unruh radiation is negative and smaller than that of Larmor radiation by one order in a/m, where a is the constant acceleration and m is the mass of the particle. Thus, the Unruh radiation appears to be a suppression of the classical Larmor radiation. The quantum interference effect plays an important role in this unique signature. The results is consistent with the predictions of a model consisting of a particle coupled to a massless scalar field as well as those of the previous studies on the quantum effect on the Larmor radiation.