Deep Convolutional Neural Networks (CNNs) are increasingly used in multimedia retrieval, and accelerating Deep CNNs has recently received an ever-increasing research focus. Among various approaches proposed in the literature, filter pruning has been regarded as a promising solution, which is due to its advantage in significant speedup and memory reduction of both network model and intermediate feature maps. Many works have been proposed to find unimportant filters, and then prune it for accelerating Deep CNNs. However, they mainly focus on using heuristic methods to evaluate the importance of filters, such as the statistical information of filters (e.g., prune filter with small l(2)-norm), which may be not perfect. In this paper, we propose a novel filter pruning method, namely A Unified-Model via Block Coordinate Descent for Learning the Importance of Filter (U-BCD). The importance of the filters in our U-BCD is learned by optimizing method. We can simultaneously learn the filter parameters and the importance of filters by block coordinate descent method. When applied to two image classification benchmarks, the effectiveness of our U-BCD is validated. Notably, on CIFAR-10, our U-BCD reduces more than 57% FLOPs on ResNet-110 with even 0.08% relative accuracy improvement, and also achieve state-of-the-art results on ILSVRC-2012.