Two-dimensional (2D) metal shrouded crystals, a new kind of conceptional materials, have attracted remarkable attentions due to their unique properties. Here, we propose a novel class of 2D metal shrouded materials, tetragonal transition-metal phosphide (TM2P), which show peculiar features of coexistence of in-plane TM-P covalent bond and TM-TM interlayer metallic bonds. From combined of high throughput searching and first-principles calculations, Fe2P, Co2P, Ni2P, Ru2P, and Pd2P monolayer sheets stand out because they simultaneously have high thermal, dynamical, and mechanical stability. All these five TM2P materials are metals, especially Pd2P can be a promising catalyst for hydrogen evolution reaction with very low overpotential. Moreover, these 2D TM2Ps show good ductility since they can withstand a tensile strain up to 45%. Even in the large strain range, the strengthened interlayer TM-TM metallic bonds dominate the deformation behavior, and the corresponding metallicity of 2D TM2Ps is well preserved. Due to the competition between the d-d direct exchange and d-p-d superexchange interactions, Fe2P behaves as an antiferromagnetic material with TN of 23 K, while the Co2P is a ferromagnetic material with TC of 580 K. Our results not only enrich the database of 2D metal shrouded crystals, but also provide promising candidates of novel 2D materials for multifunctional applications in nanoelectronic, spintronics and electrocatalysis.