An uncertainty evaluation is presented for the spectroradiometric measurement of the averaged LED intensity (ALI), which is a standardized photometric quantity of LEDs introduced by the Commission Internationale de l'Eclairage. Using a spectral irradiance standard lamp as a calibration source for the spectroradiometer, 12 uncertainty components are sorted out and their propagation formulated with correlations between the components taken into account. The procedure of uncertainty evaluation is demonstrated for four LED samples of different colors; red, green, blue, and white. The relative uncertainties of the ALI of the test samples are determined to be in a range from 4.1% to 5.5% (k=2), but most of their dominant uncertainty components turn out to be systematic and correlated. In conclusion, correlations between the uncertainty components critically affect the overall uncertainty of the LED measurement using a spectroradiometer.