We present observations with the new 11-GHz radiometer of the COSMOSOMAS experiment at the Teide Observatory (Tenerife). The sky region between 0° <= RA <= 360° and 26° <= Dec. <= 49° (ca. 6500 deg2) was observed with an angular resolution of . Two orthogonal independent channels in the receiving system measured total power signals from linear polarizations with a 2-GHz bandwidth. Maps with an average sensitivity of 50 μK per beam have been obtained for each channel. At high Galactic latitude (|b| > 30°) the 11-GHz data are found to contain the expected cosmic microwave background (CMB) as well as extragalactic radiosources, galactic synchrotron and free-free emission, and a dust-correlated component which is likely of Galactic origin. At the angular scales allowed by the window function of the experiment, the 100-240 μm dust-correlated component presents an amplitude ΔT ~ 9-13 μK while the CMB signal is of the order of 27 μK. The spectral behaviour of the dust-correlated signal is examined in the light of previous COSMOSOMAS data at 13-17 GHz and Wilkinson Microwave Anisotropy Probe data at 22-94 GHz in the same sky region. We detect a flattening in the spectral index of this signal below 20 GHz which rules out synchrotron radiation as being responsible for the emission. This anomalous dust emission can be described by a combination of free-free emission and spinning dust models with a flux density peaking around 20 GHz.