We studied the nonlinear estimation problem of extended Kalman filter and appled this method to LEO satellite system. Through this method the performance of extended Kalman filter was analyzed. There were certain presumption taken; J2 and atmospheric drag were simply considered in the dynamic model of LEO satellite and the system noise error of $sigma_r$=150m, $sigma_r$=10m/s was presumed in the observation data. As results of this simulation, the overall state estimation errors of extended Kalman filter were within the presumed error range and also the ability of performance was maximized when the condition was the state process noise Q has the 1/10 level of covariance matrix Po.