One of the challenges in the field of perovskite solar cells (PSC) is the development of inorganic hole-transporting-materials (HTM) suitable for solution-processed deposition, in order to have cheaper, more stable and scalable devices. Herein, we report the synthesis and characterization of p-type copper sulfide nanoparticles for their application for the first time as a low-cost, fully-inorganic HTM in mesoscopic n-i-p PSC. By employing CuS combined with two different perovskites, CH3NH3PbI3 (MAPbI(3)) and (FAPbI(3))(0.78)(MAPbBr(3))(0.14)(CsPbI3)(0.08) (CsFAMAPbIBr), very high current densities and fill-factors are observed, suggesting an effective hole-extraction happening at the CuS interface. Noticeable, our cells exhibit one of the highest power conversion efficiencies (PCE) in n-i-p configuration employing a sole solution-processed inorganic HTM via non-toxic solvents, leading to 13.47% and 11.85% for MAPbI(3) and CsFAMAPbIBr, respectively. As a remark, such PCE values are only limited by a reduced open-circuit voltage around 0.8 V, due to different phenomena occurring at perovkite/CuS interface such as an increased non-radiative recombination, caused by considerable difference in valence band value, and the effect of CuS metallic character. Overall, these findings highlight CuS as an extremely cheap alternative to common organic HTMs and pave the way to new improvements employing this material in full-inorganic blocking layers PSC.