The pressure-temperature-field phase diagram and quantum fluctuation effect were investigated in the itinerant ferromagnet U3P4 by resistivity, ac susceptibility, and Hall effect measurements under high pressure. The zerotemperature ferromagnetic-to-paramagnetic transition is located at Pc ∼ 4.0 GPa. The tricritical point exists at P∗ = 3.8 GPa and T∗ = 32K, where the ferromagnetic transition changes from second- to first-order. As a quantum fluctuation effect, the low-temperature resistivity at Pc follows T5/3 dependence, which was theoretically described in the case of a three-dimensional ferromagnet. This result indicates that the ferromagnetic-to-paramagnetic transition at Pc may be considered as weakly first-order. Another critical behavior, the huge enhancement of ρ0 observed at Pc, cannot be interpreted as the ferromagnetic fluctuation effect. The Hall effect measurements suggest that the magnetic structure in the ordered state changes under high pressure.