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We define a complete sample of thirty-three GHz-Peaked-Spectrum (GPS) radiosources based on their spectral properties. We present measurements of theradio spectra and polarization of the complete sample and a list of additionalGPS sources which fail one or more criteria to be included in the completesample. The majority of the data have been obtained from quasi-simultaneousmulti-frequency observations at the Very Large Array (VLA) during 3 observingsessions. Low frequency data from the Westerbork Synthesis Radio Telescope(WSRT) and from the literature have been combined with the VLA data in order tobetter define the spectral shape.  The objects presented here show a rather wide range of spectral indices athigh and low frequencies, including a few cases where the spectral index belowthe turnover is close to the theoretical value of 2.5 typical of self-absorbedincoherent synchrotron emission. Faint and diffuse extended emission is foundin about 10% of the sources. In the majority of the GPS sources, the fractionalpolarization is found to be very low, consistent with the residual instrumentalpolarization of 0.3%.Comment: 23 pages, 16 figures, uses psfig.sty, A&AS in pres

A complete sample of GHz-peaked-spectrum radio sources and its radio properties