Hybrid improper ferroelectricity (HIF) is recognized as a secondary ferroelectric phenomenon induced by coupling of in-plane rotation and out-of-plane tilt of anion octahedra in compounds with the units of perovskite structure. HIF is expected to be applicable in the multiferroic materials with strong magnetoelectric coupling owing to its intrinsic characteristic for electric-field control of magnetism, thereby greatly extending the connotation and denotation of ferroelectric physics. This paper focuses on the experimental progress of HIF materials with Ruddlesden-Popper (R-P) structure. It also establishes the linear relationship between Curie temperature (T_C) and tolerance factor (τ) of double-layered R-P oxides, elucidating the underlying physical mechanisms of HIF. Based on intrinsic electric-field control of magnetism for HIF, the detection of coexistence of polar and weak ferromagnetic phases in ferrites with double-layered R-P structures is of great scientific significance. Additionally, the documented ferroelectricity in the A-site cation-ordered triple-layered R-P oxide has significantly expanded the fields of HIF. Although significant progress has been achieved in understanding HIF in R-P oxides, more efforts should be made to explore more new material systems and single-phase multiferroic materials.