We tackle the problem of establishing dense correspondences between a pair of images in an efficient way. Most existing dense matching methods use 4D convolutions to filter incorrect matches, but 4D convolutions are highly inefficient due to their quadratic complexity. Besides, these methods learn features with fixed convolutions which cannot make learnt features robust to different challenge scenarios. To deal with these issues, we propose an Efficient Dynamic Correspondence Network (EDCNet) by jointly equipping pre-separate convolution (Psconv) and dynamic convolution (Dyconv) to establish dense correspondences in a coarse-to-fine manner. The proposed EDCNet enjoys several merits. First, two well-designed modules including a neighbourhood aggregation (NA) module and a dynamic feature learning (DFL) module are combined elegantly in the coarse-to-fine architecture, which is efficient and effective to establish both reliable and accurate correspondences. Second, the proposed NA module maintains linear complexity, showing its high efficiency. And our proposed DFL module has better flexibility to learn features robust to different challenges. Extensive experimental results show that our algorithm performs favorably against state-of-the-art methods on three challenging datasets including HPatches, Aachen Day-Night and InLoc.