In this paper, we discuss the initial acquisition of the code division multiplexed DS/SS down-link signals at a user terminal of multiple LEO mobile satellite communication systems. In LEO systems, a receiver generally receives signals from plural satellites for soft hand-off and for satellite diversity as a countermeasure to shadowing. In this situation, the signal from each satellite becomes the interference to the signals from other satellites. In addition to this inter-satellite interference, we have to consider the intra-satellite interference from user channels to a pilot channel because of the loss of orthogonality of channels at initial acquisition stage especially under frequency offsets due to Doppler effect. Thus in this paper, we analytically evaluate the performance of an initial acquisition scheme, taking the intra/inter-satellite interference under Doppler shift into account.