In the tracking system, a better prediction model can significantly reduce power consumption in a wireless sensor network because fewer redundant sensors will be activated to keep monitoring the object. The Gauss-Markov mobility model is one of the best mobility models to describe object trajectory because it can capture the correlation of object velocity in time. Traditionally, the Gauss-Markov parameters are estimated using an autocorrelation technique or a recursive least-squares estimation technique; either of these techniques, however, requires a large amount of historical movement information of the mobile object, which is not suitable for tracking objects in a wireless sensor network because they demand a considerable amount of message communication overhead between wireless sensors which are usually battery powered. In this paper, we develop a Gauss-Markov parameter estimator for wireless sensor networks (GMPE_MLH) using a maximum likelihood technique. The GMPE_MLH model estimates the Gauss-Markov parameters with few requirements in terms of message communication overhead. Simulations demonstrate that the GMPE_MLH model generates negligible differences between the actual and estimated values of the Gauss-Markov parameters and provides comparable prediction of the mobile object's location to the Gauss-Markov parameter estimators using an autocorrelation technique or a recursive least-squares estimation.