On the basis of determining the ordering of Co and Mn atoms in the Y(Mn1-xCox)12 alloys, we went on to carry out the neutron diffraction measurement of these compounds at liquid nitrogen temperture to investigate their magnetic structure. Some magnetic superstructure peaks were observed, which can be indexed as h+k+l=2n+1 based on the YMn12-type unit cell. The experimental data were analysed using various possible magnetic structure models. From the best fit between the calculated and observed intensities, it is concluded that: (A) Y(Mn1-xCox)12 are antiferromagnetic structure of noncollinear type for x = 0, 0.3 and 0.4; The arrangement of partial magnetic moments on 8f and 8j sites change into parallel to each other for x = 0.5, 0.6 and 0.67. Whereas the magnetic moments on 8i sites still remain in antiparallel configuration. Moreover, the ratio of ferromagnetic composition increases with the increase of Co concentration x; All magnetic moments on 8i, 8j and 8f sites are parallel to each other in the basal plane of the tetragonal structure for x = 0.8. The sample exhibits ferromagnetism in such a case. (B) As compared with the YMn12, the substitution of Mn with Co leads to an increase of the mean magnetic moment on 8i, 8j and 8f atoms.