Transition-metal (TM) phosphides attract increasing attention with applications for energy conversion and storage, due to their outstanding physical, chemical, and electronic properties. The 3d transition metal tetraphosphides (TMP, TM = V, Cr, Mn, and Fe) possess multiple allotropies and rich electronic properties. Here, we perform the investigations of the structural, electronic, and elastic properties for 3d-TMP (TM = V, Cr, Mn, and Fe) using density functional theory (DFT) calculations. These compounds are featured with alternating buckled phosphorus sheets with ten-numbered phosphorus rings and varied transition-metal layers. Hybrid DFT calculations reveal that TMP compounds exhibit a wide range of electrical properties, ranging from metallic behavior for VP to semiconducting behavior for CrP with the narrow direct band gap of 0.63 eV to enlarged semiconducting MnP and FeP with band gap of 1.6-2.1 eV. The bonding analysis indicates that P-P and TM-P covalent interactions dominate in the phosphorus sheets and TMP octahedrons, which are responsible for the structural and electronic diversity.