We present the first study of a magnetic quantum phase transition in the itinerant-electron ferromagnet Ni3Al at high pressures. Electrical resistivity measurements in a diamond anvil cell at hydrostatic pressures up to 100 kbar and temperatures as low as 50 mK indicate that the Curie temperature collapses towards absolute zero at a critical pressure pc=82(2) kbar. Over wide ranges in pressure and temperature, both in the ferromagnetic and paramagnetic states, the temperature variation of the resistivity is found to deviate from the conventional Fermi-liquid form. We consider the extent to which this deviation can be understood in terms of a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions.