We report on a survey of the inner part of the Galactic Plane in very high energy gamma-rays, with the H.E.S.S. Cherenkov telescope system. The Galactic Plane between +-30deg in longitude and +-3deg in latitude relative to the Galactic Centre was observed in 500 pointings for a total of 230 hours, reaching an average flux sensitivity of 2% of the Crab Nebula at energies above 200 GeV. Fourteen previously unknown sources were detected at a significance level greater than 4 sigma after accounting for all trials involved in the search. Initial results on the eight most significant of these sources were already reported elsewhere. Here we present detailed spectral and morphological information for all the new sources, along with a discussion on possible counterparts in other wavelength bands. The distribution in Galactic latitude of the detected sources appears to be consistent with a scale height in the Galactic disk for the parent population smaller than 100 pc, consistent with expectations for supernova remnants and/or pulsar wind nebulae