We report new interferometric observations of IRAS 04368 + 2557 (L1527) in (CO)-C-13 (J = 1-0), (CO)-O-18 (J = 1-0), and 2.7 mm continuum emission using the Nobeyama Millimeter Array. The continuum map shows a well-defined emission peak with slightly extended features. The extended features are consistent with an 800 mu m continuum map. The (CO)-C-13 map shows blueshifted and redshifted outflowing shells characterized by a bipolar V-shape structure with a wide opening angle toward the east and west of the central source. Near the systemic velocity, a slightly blueshifted X-shaped condensation was detected in (CO)-C-13 with its peak coincident with the central source. The symmetrical distribution of the X-shaped condensation centered on the central source suggests that it is a circumstellar envelope surrounding the central source. The (CO)-O-18 map shows a flattened structure elongated in the north-south direction, perpendicular to the outflow axis, centered on the central source. This flattened structure correlates spatially with the (CO)-C-13 X-shaped condensation. Both eastern and western edges of the flattened structure are concave, as the (CO)-C-13 X-shaped condensation also shows, and they are spatially well anticorrelated with the distribution of the outflowing shells in both blueshifted and redshifted velocities. The flattened structure is hence naturally interpreted as a disklike flattened envelope with an almost edge-on configuration. Its radius and gas mass are estimated to be similar to 2000 AU and similar to 0.038 M., respectively. The edge-on flattened envelope has both rotational and radial motions with the latter dominant. The large specific angular momentum carried by the envelope gas implies that the radial motion can be infall rather than outflow. The infall and rotation velocities are similar to 0.3 km s(-1) and similar to 0.05 km s(-1), respectively, at the envelope radius of 2000 AU. The flattened envelope is clearly not supported by rotation, but it is dynamically infalling. Its mass infall rate is similar to 1.1 x 10(-6) M. yr(-1) at 2000 AU in radius. This mass infall rate is consistent with that estimated from the bolometric luminosity of 1.4 L. and the mass of 0.1 M. of the central star. On the assumption that the mass infall rate is constant with time, the age of the central star is estimated to be similar to 10(5) yr, which is comparable to the typical age of protostars in Taurus, even though the central star in L1527 is identified as a very young class O source. The rotating motion of the flattened envelope is opposite to the large-scale rotation of the L1527 cloud, suggesting that the rotation of the flattened envelope did not originate from the large-scale rotation.