The energy spectra in water phantom for the therapeutic high-energy X-ray beams are not easy to determine because the experimental methods are very difficult to perform whereas the Monte Carlo calculations need the suitable computer power. This fact is evidenced by the lack of extensive data including the energy spectra in water. Even dosimetry protocols do not include such kind of information. Authors present usually X-ray spectra determined in air in the vicinity. However, the spectra in air cannot be generally used to characterize accurately the beam quality in another irradiated medium. The energy spectra for the 6MV X-ray beam were determined along the beam central-axis in water - a medium recommended by the dosimetry protocols. The spectra were derived using the Monte Carlo method for open and wedged radiation fields of 3cm x 3cm and 10cm x 10cm. The GEANT4 code with the LowEnergy models of interactions of photons with matter was applied for the calculations. All calculations were performed under the linux operation system, on computers in the Department of Nuclear Physics and Its Application of Institute of Physics of University of Silesia in Katowice (Poland). The calculations were realized by the computer simulations. The simulation program was verified by the comparison of the calculated depth-dose characteristics in water with those measured with the use of the Markus ionization chamber. The spectra were calculated in the range of the depths up to 27.35cm for SSD=100cm. This work showed that the shapes of the spectra as well as the mean energy Ed of the beam depended strongly on the radiation field size, depth d in water phantom and appearance of the wedge. In the case of the 3cm x 3cm field, Ed increases with the increasing depth d and it ranges from 1.720MeV to 2.192MeV for the open field and from 1.845MeV to 2.276MeV for the wedged field. A decrease of the mean energy is observed for larger radiation fields. In the case of the 10cm x 10cm open field, Ed decreases as the depth increases up to d=6cm (E0.1cm=1.591MeV, E0.1cm/E6.1cm=1.070) and it increases past the depth of d=9cm (E9.1cm=1.488MeV, E9.1cm/E27.35cm=0.921). Analogous dependence appears for the wedged 10 cm x 10 cm field. Ed decreases with the increasing depth up to d=6cm (E0.1cm=1.721MeV, E0.1cm/E6.1cm=1.076) and then Ed increases past the depth of d=9cm (E9.1cm=1.596MeV, E9.1cm/E27.35cm=0.940). Shape of the characteristics of Ed(d) in water are similar for the open as well as the wedged radiation fields. However, the use of the wedge makes energy greater of about 0.1MeV. The detailed knowledge of the energy spectra of therapeutic beams from medical linacs is essential for the calculations of the stopping power ratios or the beam quality correction factors, for dose calculation algorithms in advanced treatment planning, for investigations of treatment machine head design etc.