We have identified local analogs of strong $H{alpha}$ Emitters (HAEs) that dominate the z~4 Lyman-break galaxy population using the Sloan Digital Sky Survey (SDSS). At z<0.4, only 0.04% of galaxies are classified as HAEs with $H{alpha}$ equivalent width larger than $500{AA}$, comparable to that of z~4 HAEs. The $H{alpha}$-to-UV luminosity ratio of local HAEs is consistent with that of z~4 HAEs, indicating relatively large specific star formation rate in these galaxies compared to traditionally studied UV-selected Lyman break analogs. Local HAEs are young, less evolved galaxies with low metallicity. It is still difficult to constrain whether the star formation in local HAEs is powered by minor mergers or by cosmological cold gas accretion. However, the stacked optical spectrum of local HAEs shows several strong ionization lines, for example HeII 4686 emission line, which are shown in Wolf-Rayet galaxies. Thus it is highly likely that local HAEs are galaxies with an elevated ionization parameter, either due to a high electron density or large escape fraction of hydrogen ionizing photons.