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 zero-temperature ferromagnetic-to-paramagnetic transition is located at P-c similar to 4.0 GPa. The tricritical point exists at P* = 3.8 GPa and T* = 32 K, where the ferromagnetic transition changes from second- to first-order. As a quantum fluctuation effect, the low-temperature resistivity at P-c follows T-5/3 dependence, which was theoretically described in the case of a three-dimensional ferromagnet. This result indicates that the ferromagnetic-to-paramagnetic transition at P-c may be considered as weakly first-order. Another critical behavior, the huge enhancement of rho(0) observed at P-c, 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.