The new Max-Count aggregation operator presented finds the maximum number of 2D moving points that overlap a moving query rectangle within a specified time interval. Two linearly moving points define the query rectangle which may move, and grow or shrink over time. We give the first constant running-time estimation algorithm to solve the Max-Count aggregation problem in two dimensions. The estimation algorithm uses 4-dimensional buckets to index objects. The implementation of the Max-Count estimation algorithm and the experimental data show that the method exhibits good accuracy and speed.