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This paper aims to improve security performance of data transmission with a mobile eavesdropper in a wireless network. The instantaneous channel state information (CSI) of the mobile eavesdropper is unknown to legitimate users during the communication process. Different from existing work, we intend to reduce power consumption of friendly jamming signals. Motivated by the goal, this work presents a location-based prediction scheme to predict where the eavesdropper will be later and to decide whether a friendly jamming measure should be selected against the eavesdropper. The legitimate users only take the measure when the prediction result shows that there will be a risk during data transmission. According to the proposed method, system power can be saved to a large degree. Particularly, we first derive the expression of the secrecy outage probability and set a secrecy performance target. After providing a Markov mobile model of an eavesdropper, we design a prediction scheme to predict its location, so as to decide whether to employ cooperative jamming or not, and then design a power allocation scheme and a fast suboptimal helper selection method to achieve targeted and efficient cooperative jamming. Finally, numerical simulation results demonstrate the effectiveness of the proposed schemes.