We describe the first instrument of a cosmic microwave background experiment for mapping cosmological structures on medium angular scales (the COSMOSOMAS experiment) and diffuse Galactic emission. The instrument is located at Teide Observatory (Tenerife) and is based on a circular scanning sky strategy. It consists of a 1-Hz spinning flat mirror directing the sky radiation into a 1.8-m off-axis paraboloidal antenna, which focuses it on to a cryogenically cooled HEMT-based receiver operating in the frequency range 12-18GHz. The signal is split by a set of three filters, allowing simultaneous observations at 13, 15 and 17GHz, each with a 1-GHz bandpass. A 1°-5° resolution sky map complete in right ascension and covering 20° in declination is obtained each day at these frequencies. The observations presented here correspond to the first months of operation, which have provided a map of 9000deg2 on the sky centred at Dec.=+31° with sensitivities of 140, 150 and 250μK per beam area in the channels at 13, 15 and 17GHz, respectively. We discuss the design and performance of the instrument, the atmospheric effects, the reliability of the data obtained and prospects of achieving a sensitivity of 30μK per beam in 2 years of operation.