On the basis of the intrinsic sparsity of sea clutter in shipborne high‐frequency surface wave radar, a joint sparse recovery‐based space–time adaptive processing (STAP) technique is proposed to suppress the spread sea clutter. In the proposed method, the partial clutter subspace is first estimated with training samples from only one range cell. Afterwards, a generalised matching pursuit method using the oblique projector is derived to recover the complementary clutter subspace. The sea clutter suppressor is finally constructed by STAP. According to experimental results, the proposed method can obtain a more accurate estimation of sea clutter spectrum and thus achieve better suppression performance.