To address the scale variance and uneven distribution of objects in scenarios of object-counting tasks, an algorithm called Refinement Network (RefNet) is exploited. The proposed top-down scheme sequentially aggregates multiscale features, which are laterally connected with low-level information. Trained by a multiresolution density regression loss, a set of intermediate-density maps are estimated on each scale in a multiscale feature pyramid, and the detailed information of the density map is gradually added through coarse-to-fine granular refinement progress to predict the final density map. We evaluate our RefNet on three crowd-counting benchmark datasets, namely, ShanghaiTech, UCF $\mathrm{\_}$CC $\mathrm{\_}$50, and UCSD, and our method achieves competitive performances on the mean absolute error and root mean squared error compared to the state-of-the-art approaches. We further extend our RefNet to cell counting, illustrating its effectiveness on relative counting tasks.