Alfven waves, produced on the ground by artificial or by soundstorm, propagating to the near-earth space along the geomagnetic field lines, would decay greatly with distance. A dipole geomagnetic field model in near earth space, plasma density and conductivity models derived from observational data are used in this study to investigate the attenuation of Alfven waves below 1000 km altitude by numerical simulation methods. The frequency that would be detected by magnetometer carried by satellite was also found. The result showed that: Alfven waves will decay sharply in the height of less than 50 km for the much weak electrical conductivity in this region; it is 0.4 Hz Alfven waves, when transmitted to 1000 km, that becomes about one-thousandth of the original, so Alfven waves below 0.4 Hz can be detected by LEO satellites.