A Monte Carlo code, MORSE-CV, which can calculate the covariance of the scalar neutron flux spectrum, was developed. Integral values and their variances calculated from the spectrum and its covariance were compared with the corresponding values calculated directly using the Monte Carlo method. The integral value calculated from the spectrum agreed well with the directly calculated value. Their standard deviations also agreed well with each other when the spectral correlation between different energies was treated correctly. When the correlation was ignored, the deviation was about one-half of the former value.