The updated H-band spectral-line list (from lambda 15000-17000) adopted by the Apache Point Observatory Galactic Evolution Experiment (APOGEE) for the SDSS-IV Data Release 16 (DR16) is presented in this work. The APOGEE line list is a combination of atomic and molecular lines, with data drawn from laboratory, theoretical, and astrophysical sources. Oscillator strengths and damping constants are adjusted using high signal-to-noise, high-resolution spectra of the Sun, and alpha Boo (Arcturus), as "standard stars." Updates to the DR16 line list, as compared to the previous DR14 version, include the addition of molecular H2O and FeH lines, as well as a much larger (by a factor of similar to 4) atomic line list, including a significantly greater number of transitions with hyperfine splitting. More recent references and line lists for the crucial molecules, CO and OH, as well as for C-2 and SiH, are also included. In contrast to DR14, DR16 contains measurable lines from the heavy neutron-capture elements cerium (as Ce ii), neodymium (as Nd ii), and ytterbium (as Yb ii), as well as one line from rubidium (as Rb i), which may be detectable in a small fraction of APOGEE red giants.