The paper describes the development of a new generation of Monte Carlo track structure code, which simulates full slowing down of low-energy alpha-particles history tracks (leahist) in the range 1 keV-8 MeV in water. All primary interactions including elastic scattering, ionization, excitation, and charge exchange by He2+, He+, and He-0 were taken into account. Cross sections for bare and dressed helium ions and neutral helium impact were obtained from experimental data for water vapor targets. Where data were lacking the existing experimental data were fitted and extrapolated. The tracks of secondary electrons were generated using the electron track code kurbuc. The code can be operated to generate tracks both in the track segment and the full-slowing-down modes. Tracks were analyzed to provide confirmation on the reliability of the code and information on physical quantities, such as range, W-values, restricted stopping power and radial dose profiles. This new development enables us to work on aspects of the radiation of environmental interests such as radon. No attempt was made to simulate the track of alpha-particles below 1keV as in this region cross sections for interactions involving electron loss and capture are severely lacking and in general the chemistry which follows the interaction of these slow ions is not well-known.