4He confined in nanoporous media is an excellent model system for studying a strongly correlated Bose liquid and solid in a confinement potential. We studied superfluidity and liquid-solid phase transition of 4He confined in a porous Gelsil glass that had nanopores 2.5 nm in diameter. The obtained pressure-temperature phase diagram is fairly unprecedented: the superfluid transition temperature approaches zero at 3.4 MPa, and the freezing pressure is enhanced by approximately 1 MPa from the bulk one. These features indicate that the confined 4He undergoes a superfluid-nonsuperfluid-solid quantum phase transition at zero temperature. The nonsuperfluid phase may be a localized Bose-condensed state in which global phase coherence is destroyed by a strong correlation between the 4He atoms or by a random potential.