In this paper, we propose an energy-efficient tracking algorithm for predicting the trajectory of a mobile radioactive target in a wireless sensor network. The sensor nodes are assumed to be capable of detecting the strength of the background radioactive radiations as well as the signals emanating from a mobile radiological dispersal device (RDD). As the individual RDD signals may not be easily distinguishable enough from the background radiation, we propose that each sensor node sum up the strength of the signals sensed in its neighborhood for a sampling time period, and then (at the end of this time period) forward the value of the sum of the signals sensed in the neighborhood to a control center (sink). The sink identifies the sensor nodes (suspect nodes) that report relatively larger values for the sum of the signal strengths that is different from those of others; the arithmetic mean of the X and Y coordinates of the suspect sensor nodes is predicted as the location of the RDD at a time instant corresponding to the middle of the sampling time period. We evaluate the difference between the predicted and exact locations of the RDD trajectory over time as a function of the different operating parameters (such as the RDD velocity, transmission and sensing range of the sensor nodes and the duration of the sampling time period) as well as evaluate the network lifetime and node lifetime incurred due to exhaustion of the energy levels of the sensor nodes.