We present new intensity and polarization observations of the Taurus molecular cloud ( TMC ) region in the frequency range 10–20 GHz with the Multi-Frequency Instrument ( MFI ) mounted on the first telescope of the QUIJOTE experiment . From the combination of the QUIJOTE data with the WMAP 9-yr data release , the Planck second data release , the DIRBE maps and ancillary data , we detect an anomalous microwave emission ( AME ) component with flux density S _ { AME,peak } = 43.0 \pm 7.9 Jy in the Taurus Molecular Cloud ( TMC ) and S _ { AME,peak } = 10.7 \pm 2.7 Jy in the dark cloud nebula L1527 , which is part of the TMC . In the TMC the diffuse AME emission peaks around a frequency of 19 GHz , compared with an emission peak about a frequency of 25 GHz in L1527 . In the TMC , the best constraint on the level of AME polarization is obtained at the Planck channel of 28.4 GHz , with an upper limit \pi _ { AME } < 4.2 \% ( 95 \% C. L. ) , which reduces to \pi _ { AME } < 3.8 \% ( 95 \% C.L . ) if the intensity of all the free–free , synchrotron and thermal dust components are negligible at this frequency . The same analysis in L1527 leads to \pi _ { AME } < 5.3 \% ( 95 \% C.L . ) , or \pi _ { AME } < 4.5 \% ( 95 \% C.L . ) under the same assumption . We find that in the TMC and L1527 on average about 80 \% of the HII gas should be mixed with thermal dust . Our analysis shows how the QUIJOTE-MFI 10–20 GHz data provides key information to properly separate the synchrotron , free–free and AME components .