We present near-infrared spectroscopy of 10 weak emission-line quasars (WLQs) at redshifts of z ∼ 2, obtained with the Palomar 200 inch Hale Telescope. WLQs are an exceptional population of type 1 quasars that exhibit weak or no broad emission lines in the ultraviolet (e.g., the C iv λ1549 line), and they display remarkable X-ray properties. We derive Hβ-based single-epoch virial black hole masses (median value 1.7 × 109 M ⊙) and Eddington ratios (median value 0.5) for our sources. We confirm the previous finding that WLQ Hβ lines, as a major low-ionization line, are not significantly weak compared to typical quasars. The most prominent feature of the WLQ optical spectra is the universally weak/absent [O iii] λ5007 emission. They also display stronger optical Fe ii emission than typical quasars. Our results favor the super-Eddington accretion scenario for WLQs, where the weak lines are a result of a soft ionizing continuum; the geometrically thick inner accretion disk and/or its associated outflow is responsible for obscuring the nuclear high-energy radiation and producing the soft ionizing continuum. We also report candidate extreme [O iii] outflows (blueshifts of ≈500 and 4900 km s−1) in one object.