Long-term variations in high-energy (greater than 2 MeV) electron flux at synchronous orbit are examined to reveal their close relationship to geomagnetic activity. The electron flux diminishes rapidly in association with an enhancement of geomagnetic activity (storm) and then increases. The flux becomes higher than pre-storm level and its peak occurs approximately 4--5 days after the enhancement of geomagnetic activity. A linear prediction filter is designed for daily sums of Kp as input data and corresponding daily averages of the electron flux (Log value) as output data. The data are those taken in 1984--1985. This filter can successfully reproduce the electron flux behavior observed not only in 1984--1985 but also in 1978--1981. ¿ American Geophysical Union 1988