A new method of line shape calculations of hydrogen-like atoms in magnetized plasmas is presented. This algorithm makes it possible to solve two fundamental problems in the broadening theory: the analytical description of the radiation transition array between excited atomic states and account of a thermal ion motion effect on the line shapes formation. The solution to the first problem is based on the semiclassical approach to dipole matrix elements calculations and the usage of the specific symmetry properises of the Coulomb field. The second one is considered in terms of the kinetic treatment of the frequency fluctuation model (FFM). As the result one has a universal description of line shapes under the action of the dynamic of ion’s microfield. The final line shape is obtained by the convolution of the ionic line shape with the Voigt electron-Doppler profile. The method is applicable formally for large values of principle quantum numbers. However, it is demonstrated the efficiency of the results even for well known first members of the hydrogen Balmer series Dalpha and Dbeta. The comparison of obtained results with accurate quantum calculations is presented. The new method may be of interest for investigations of spectral line shapes of hydrogen-like ions presented in different kinds of hot ionized environments with the presence of a magnetic field, including SoL and divertor tokamak plasmas.