Non-local attention (NLA) is a powerful technique for capturing long-range feature correlations in deep single-image super-resolution (SR). However, NLA suffers from high computational complexity and memory consumption, as it requires aggregating all non-local feature information for each query response and recalculating the similarity weight distribution for different abstraction levels of features. To address these challenges, we propose a novel learnable collaborative attention (LCoA) that introduces inductive bias into non-local modeling. Our LCoA consists of two components: learnable sparse pattern (LSP) and collaborative attention (CoA). LSP uses the k-means clustering algorithm to dynamically adjust the sparse attention pattern of deep features, which reduces the number of non-local modeling rounds compared with existing sparse solutions. CoA leverages the sparse attention pattern and weights learned by LSP and co-optimizes the similarity matrix across different abstraction levels, which avoids redundant similarity matrix calculations. The experimental results show that our LCoA can reduce the non-local modeling time by about 83% in the inference stage. In addition, we integrate our LCoA into a deep learnable collaborative attention network (LCoAN), which achieves competitive performance in terms of inference time, memory consumption, and reconstruction quality compared with other state-of-the-art SR methods. Our code and pre-trained LCoAN models were uploaded to GitHub ( https://github.com/YigangZhao/LCoAN) for validation.