Abstract Pattern synthesis of the sparse linear array (SLA) has played an important role when the antenna size is extremely limited. Although grid‐based compressed sensing (CS) algorithms have been widely utilised to synthesise the SLA, the performance is greatly affected by the grid mismatch problem. To solve the problem, a reweighted gridless CS (RGCS) algorithm based on the reweighted atomic norm minimisation and the rotational invariance propagator method is introduced. In the RGCS algorithm, the number of antenna elements can be efficiently reduced through the reweighted gridless convex optimisation, which utilises a reweighted strategy to break the limit of the atomic norm and improves the performance of the SLA. More importantly, in addition to the focussed‐beam pattern, the proposed algorithm can also synthesise the SLA with the asymmetric beam pattern. Numerical experiments show that the RGCS algorithm can save about 18.75 % –46 % array elements for the uniform linear array.