  We explore superfluidity for $^4$He confined in a porous glass which has
nanopores of 2.5 nm in diameter, at pressures up to 5 MPa. With increasing
pressure, the superfluidity is drastically suppressed, and the superfluid
transition temperature approaches 0 K at $P_c = 3.5$ MPa. The features strongly
suggest that the extreme confinement of $^4$He into the nanopores induces a
quantum phase transition from superfluid to nonsuperfluid at 0 K, and at $P_c$.
