A Gaussian distribution was parametrized for the initial distribution of the electron beam emitted from a 6MeV medical linear accelerator. A percent depth dose was measured in a water phantom and the corresponding Monte Carlo calculations were performed starting from a Gaussian distribution for a range of standard deviations, ${sigma}=0.1$, 0.15<E>, 0.2<E>, 0.25<E>, and 0.3<E> with <E> being the mean value for the Incident beam energy. When measurement and calculation were compared, the calculation with the Gaussian distribution for ${sigma}=0.25$ turned out to agree best with the measurement. The results from the present work can be utilized as input energy data in planning an electron beam therapy with a Monte Carlo calculation.