Regarding the problems of singularity while using classic orbital elements in satellite bearings-only passive tracking and the lack of physical meanings in measurement equation's variables and their corresponding coordinate transformations, a new satellite-to-satellite extended Kalman filtering (EKF) tracking method with bearings-only measurements in J2000.0 ECI frame is put forward. An explicit definition of the variables and their coordinate transformations in measurement equation are submitted. Moreover, the state propagation stage, state transfer matrix and measurement Jacobi matrix are deducted in detail. Performance is contrasted and validated through simulated data from STK6.0 with various initial state errors and angles measurement errors. Simulation indicates that it is possible to passively track low earth circular orbit satellite (e=0) by a high earth orbit satellite (quasi-geosynchronous orbit satellite) with bearings-only measurements. When the angles measurement accuracy exceeds the average angles changing magnitude, the convergence time and the tracking errors rapidly decrease. Moreover, the method also shows resilience to varying initial state errors.