We present physical properties of spectroscopically confirmed Lyα emitters (LAEs) with very large rest-frame Lyα equivalent widths EW 0 (Lyα). Although the definition of large EW 0 (Lyα) LAEs is usually difficult due to limited statistical and systematic uncertainties, we identify six LAEs selected from ∼ 3000 LAEs at z ∼ 2 with reliable measurements of EW 0 (Lyα) ≃ 200−400Å given by careful continuum determinations with our deep photometric and spectroscopic data. These large EW 0 (Lyα) LAEs do not have signatures of AGN, but notably small stellar masses of M * = 10 7−8 M ⊙ and high specific star-formation rates (star formation rate per unit galaxy stellar mass) of ∼ 100 Gyr −1 . These LAEs are characterized by the median values of L(Lyα) = 3.7 × 10 42 erg s −1 and M UV = −18.0 as well as the blue UV continuum slope of β = −2.5 ± 0.2 and the low dust extinction E(B − V ) * = 0.02 +0.04 −0.02 , which indicate a high median Lyα escape fraction of f Lyα esc = 0.68 ± 0.30. This large f Lyα esc value is explained by the low Hi column density in the ISM that is consistent with FWHM of the Lyα line, FWHM(Lyα) = 212 ± 32 km s −1 , significantly narrower than those of small EW 0 (Lyα) LAEs. Based on the stellar evolution models, our observational constraints of the large EW 0 (Lyα), the small β, and the rest-frame Heii equivalent width imply that at least a half of our large EW 0 (Lyα) LAEs would have young stellar ages of 20 Myr and very low metallicities of Z < 0.02Z ⊙ regardless of the star-formation history.