For multiple extended target tracking, the accuracy of measurement partitioning directly affects the target tracking performance, so the existing partitioning algorithms tend to use as many partitions as possible to obtain accurate estimates of target number and states. Unfortunately, this may create an intolerable computational burden. What is worse is that the measurement partitioning problem of closely spaced targets is still challenging and difficult to solve well. In view of this, a prediction-driven measurement sub-partitioning (PMS) algorithm is first proposed, in which target predictions are fully utilized to determine the clustering centers for obtaining accurate partitioning results. Due to its concise mathematical forms and favorable properties, redundant measurement partitions can be eliminated so that the computational burden is largely reduced. More importantly, the unreasonable target predictions may be marked and replaced by PMS for solving the so-called cardinality underestimation problem without adding extra measurement partitions. PMS is simple to implement, and based on it, an effective multiple closely spaced extended target tracking approach is easily obtained. Simulation results verify the benefit of what we proposed—it has a much faster tracking speed without degrading the performance compared with other approaches, especially in a closely spaced target tracking scenario.