We analyze archival Ly alpha spectra of 12 "Green Pea" galaxies observed with the Hubble Space Telescope, model their Ly alpha profiles with radiative transfer models, and explore the dependence of the Ly alpha escape fraction on various properties. Green Pea galaxies are nearby compact starburst galaxies with [O III] lambda 5007 equivalent widths (EWs) of hundreds of angstrom. All 12 Green Pea galaxies in our sample show Ly alpha lines in emission, with an Ly alpha EW distribution similar to high-redshift Ly alpha emitters. Combining the optical and UV spectra of Green Pea galaxies, we estimate their Ly alpha escape fractions and find correlations between Ly alpha escape fraction and kinematic features of Ly alpha profiles. The escape fraction of Ly alpha in these galaxies ranges from 1.4% to 67%. We also find that the Ly alpha escape fraction depends strongly on metallicity and moderately on dust extinction. We compare their high-quality Ly alpha profiles with single H I shell radiative transfer models and find that the Ly alpha escape fraction anticorrelates with the derived H I column densities. Single-shell models fit most Ly alpha profiles well, but not the ones with the. highest escape fractions of Ly alpha. Our results suggest that low H I column density and low metallicity are essential for Ly alpha escape. and make a galaxy an Ly alpha emitter.