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 (TMP4, 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 4 (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 4 compounds exhibit a wide range of electrical properties, ranging from metallic behavior for VP 4 to semiconducting behavior for CrP4 with the narrow direct band gap of 0.63 eV to enlarged semiconducting MnP4 and FeP4, 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 TMP6 octahedrons, which are responsible for the structural and electronic diversity.