ABSTRACT This letter addresses the joint sparse recovery (JSR) problem with multiple measurement vectors (MMV) in compressive sensing (CS). Be aware of the limitations of the model‐driven methods and the advantages of the latest data‐driven approaches; the authors transform the MMV problem into sequence modelling. In this letter, the authors propose a data‐driven method, which relies on a self‐attention mechanism to automatically capture the sparse structure within and between sparse vectors. A framework of Bayesian Compressed Sensing (BCS) is then used to reconstruct the sparse vectors. The results of numerical experiments which were conducted on real‐world datasets are presented and analysed to show potential advantages of the proposed method compared with the latest MMV recovery algorithms.