Navigation of mobile wireless sensor networks and fast target acquisition without a map are two challenging problems in search and rescue applications. In this paper, we propose and evaluate a novel Gradient Driven method, called GraDrive. Our approach integrates per-node prediction with global collaborative prediction to estimate the position of a stationary target and to direct mobile nodes towards the target along the shortest path. We demonstrate that a high accuracy in localization can be achieved much faster than other random work models without any assistance from stationary sensor networks. We evaluate our model through a light-intensity matching experiment in MicaZ motes, which indicates that our model works well in a wireless sensor network environment. Through simulation, we demonstrate almost a 40% reduction in the target acquisition time, compared to a random walk model, while obtaining less than 2 unit error in target position estimation.