Background and Objectives: CR-39 plastic material with the chemical formula C10H18O7, addition to various scientific and research applications is the best option for medical lens. The color of CR-39 color changes by to laser irradiation and high-energy photons. CR-39 is also very sensitive to alpha radiation. Tracks make because stopping of alpha particle in CR-39. Along the every track, CR-39 is changed and its surface is damaged. The air contains radioactive radon gas that with progeny are famous as alpha particles emitter. Alpha that is decayed by radon and progeny, affect the performance of CR-39 plastics and remained tracks damage it. In this paper will try to use the Monte Carlo method, to simulate the density of damaged tracks and the depth of this damge in CR-39 that is produce by radon and progeny activity.Methods: In this simulation we need the data of stopping power of Alfa in air CR-39. This data are drawn from SRIM 2008 software. Radon in the air that is moving in a random place will randomly decay. Consequently, the alpha particles that arrived to CR-39 have a wide energy spectrum. By this simulation, the angle and energy spectrum of alpha particles that are descended on CR-39 is obtained introducing a new method trying to draw the CR-39 alpha particle range as a function of descended alpha particle energy. Activity of radon progeny is not equal with radon activity. The ratio of Radon progeny Activity’s to radon activity ratio (or equilibrium factor) is taken really.Result: Tracks are different angles, but maximum population is in 300 angles. Depth of damage caused by daily activities of radon is 35 mm. In depth of 15-25 mm that the track density is a little fluctuation, every track is corresponding with 100 Bq/m3 due to daily radon activity. Track density in this simulation is equal 0.142 (Track/cm2)/ (Bq.d/m3) that coincides with experimental results that reports by Lopez and et al.Conclusion: In medical application of CR-39, damages that produce by radon and progeny, gradually cause opaque lens, loss in resolution, change in refract index and finally produce light scattering in CR-39 plastic.