Using ~1700000 target- and sky-fibre spectra from the Sloan Digital Sky Survey (SDSS), we have carried out a systematic search for Galactic planetary nebulae (PNe) via detections of the [OIII] {lambda}{lambda}4959, 5007 lines. Thanks to the excellent sensitivity of the SDSS spectroscopic surveys, this is by far the deepest search for PNe ever taken, reaching a surface brightness of the [OIII] {lambda}5007 line down to about 29.0mag/arcsec^2^. The search leads to the recovery of 13 previously known PNe in the Northern and Southern Galactic Caps. In total, 44 new PN candidates are identified, including seven candidates of multiple detections and 37 candidates of single detection. The seven candidates of multiple detections are all extremely large (between 21 and 154arcmin) and faint, located mostly in the low Galactic latitude region and with a kinematics similar to disc stars. After checking their images in H{alpha} and other bands, three of them are probably HII regions, one is probably associated with a new supernova remnant, another one is possibly a true PN and the remaining two could be either PNe or supernova remnants. Based on sky positions and kinematics, seven candidates of single detection probably belong to the halo population. If confirmed, they will increase the number of known PNe in the Galactic halo significantly. All the newly identified PN candidates are very faint, with a surface brightness of the [OIII] {lambda}5007 line between 27.0-30.0mag/arcsec^2^, and very challenging to be discovered with previously employed techniques (e.g. slitless spectroscopy, narrow-band imaging), and thus may greatly increase the number of `missing' faint PNe. Our results demonstrate the power of large-scale fibre spectroscopy in hunting for ultrafaint PNe and other types of emission line nebulae. Combining the large spectral data bases provided by the SDSS and other on-going projects (e.g. the LAMOST Galactic surveys), it is possible to build a statistically meaningful sample of ultrafaint, large, evolved PNe, thus, improving the census of Galactic PNe.