We have studied various spontaneous and magnetic-field-induced phase transitions in single crystals of multiferroic Mn0.9Co0.1WO4 using magnetic and magnetoelectric measurements and neutron diffraction. Compared to pure MnWO4, our data consistently confirm that the anisotropic Co2+ ions induce reorientation of the spin cycloid structure to the ac plane and reveal Pa and Pc components of spontaneous electric polarization.Field-induced phase transitions accompanied by anomalies of magnetic susceptibility and suppression of both Pa and Pc polarizations have been observed for H∥c (∼3 T) and H∥a (∼8.5 T). Neutron diffraction has revealed that in both cases the spin cycloid plane flops in direction almost perpendicular to H, i.e., close to the ab and bc planes, respectively. Parameters describing the magnetic structures including wave vectors, orientations of the main elliptical axes, etc., have been determined in all spontaneous and field-induced states.