There is provided a radiation detector and a method of detecting radiation capable of more accurately correct fluorescence pileup. A table T in which the peak value h and the time course Tc of the intensity of fluorescence are related is previously prepared before radiation detection. The table T is based on actually-measured variation with time of the fluorescence intensity, and therefore faithfully represents the variation with time of fluorescence. When the occurrence of pileup is determined, the time course Tc corresponding to the peak value h immediately before the occurrence of the pileup is read out, and the time course Tc is subtracted from variation with time of the intensity data D to thereby estimate variation with time of the intensity of fluorescence after the occurrence of the pileup.