Due to the unique properties and diverse applications, two-dimensional (2D) nanomaterials have been widely investigated in these years. In this work, a group of new pentagonal 2D transitional-metal sulphide monolayers (MS, M = Fe, Mn, and V) are designed based on density-functional-theory (DFT) calculations. We show that all three monolayer structures are thermally, dynamically and mechanically stable. We find that FeS, MnS and VS are metallic, and FeS and MnS are also magnetic, in which the magnetic moments are contributed by the Fe and Mn atoms, respectively. We further find that these MS monolayers show high activities for hydrogen evolution reactions (HER) as the calculated Gibbs free energies are close to zero electron volt (eV), especially for FeS and VS. Our findings broaden the family of noble-metal-free two-dimensional materials, and also help to develop low cost commercial HER catalysts.