An electron beam dose calculation algorithm has been developed which is based on a superposition of pregenerated Monte Carlo electron track kernels. Electrons are transported through media of varying density and atomic number using electron tracks produced in water. The perturbation of the electron fluence due to each material encountered by the electrons is explicitly accounted for by considering the effect of (i) varying stopping power, (ii) scattering power, and (iii) radiation yield. For each step of every electron track, these parameters affect the step length, the step direction, and for energy deposited in that step respectively. Dose distributions in both homogeneous water and nonwaterlike phantoms, and heterogeneous phantoms show consistent agreement with "standard" Monte Carlo results. For the same statistical uncertainty in broad beam geometries, this new calculation method uses a factor of 9 less computation time than a full Monte Carlo simulation.