On the basis of the correlation between the solar wind and radiation belt electron fluxes, we develop a model to simulate the MeV electron phase space density variations from L = 3 to L = 8 by extending the Li et al. (2001) radial diffusion model for geosynchronous electrons. We add L dependence to the Li et al. model and allow for comparison with measurements at more than one L shell while retaining a similar form of their diffusion coefficient. The extended model achieves a prediction efficiency (PE) of 0.61 at L = 4 and 0.52 at L = 6 when the phase space density is converted to differential flux and compared with orbit-averaged Polar 2 MeV measurements at L = 4 and daily averaged LANL 0.7--1.8 MeV geosynchronous measurements for the year 1998. These results indicate that radial diffusion plays a strong role in the enhancement of radiation belt electrons yet leaves a significant portion of the variance unaccounted for. We have also tuned parameters to model the electron fluxes during four individual geomagnetic storms during 1998 and found that the parameter values must differ from those of the long term and from each other to achieve the best PE. This suggests that the different solar wind drivers have varying degrees of influence on the MeV electron variations during different magnetic storms. This model can be used to forecast the MeV electron variations inside geosynchronous orbit with a reasonably good PE on the basis of real-time solar wind measurements only.