We report new follow-up spectroscopy of i-dropout galaxies with an NB921-band depression found in the Subaru Deep Field. The NB921-depressed i-dropout selection method is expected to select galaxies with large equivalent width Ly alpha emission over a wide redshift range, 6.0<z<6.5. Two of four observed targets show a strong emission line with a clear asymmetric profile, identified as Ly alpha emitters at z=6.11 and 6.00. Their rest-frame equivalent widths are 153A and 114A, which are lower limits on the intrinsic equivalent widths. Through our spectroscopic observations (including previous ones) of NB921-depressed i-dropout galaxies, we identified 5 galaxies in total with a rest-frame equivalent width larger than 100A at 6.0<z<6.5 out of 8 photometric candidates, which suggests that the NB921-depressed i-dropout selection method is possibly an efficient way to search for Ly alpha emitters with a large Ly alpha equivalent width, in a wider redshift range than usual narrow-band excess techniques. By combining these findings with our previous observational results, we infer that the fraction of broad-band selected galaxies having a rest-frame equivalent width larger than 100A is significantly higher at z~6 (the cosmic age of ~1 Gyr) than that at z~3 (~2 Gyr), being consistent with the idea that the typical stellar population of galaxies is significantly younger at z~6 than that at z~3. The NB921-depressed i-dropout galaxies may be interesting candidates for hosts of massive, zero-metallicity Population III stars.