The mixing mechanism of axial-vectors Ds1(2460) and Ds1(2536) is studied via intermediate hadron loops, e.g. D * K, to which both states have strong couplings. By constructing the two-state mixing propagator matrix that respects the unitarity constraint and calculating the vertex coupling form factors in a chiral quark model, we can extract the masses, widths and mixing angles of the physical states. Two poles can be identified in the propagator matrix. One is at √ s = 2454.5 MeV corresponding to Ds1(2460) and the other at √ s = (2544.9 − 1.0i) MeV corresponding to Ds1(2536). For Ds1(2460), a large mixing angle θ = 47.5• between 3 P1 and 1 P1 is obtained. It is driven by the real part of the mixing matrix element and corresponds to θ = 12.3• between the j = 1/2 and j = 3/2 state mixing in the heavy quark limit. For Ds1(2536), a mixing angle θ = 39.7• which corresponds to θ = 4.4• in the heavy quark limit is found. An additional phase angle φ = −6.9• ∼ 6.9• is needed at the pole mass of Ds1(2536) since the mixing matrix elements are complex numbers. Both the real and imaginary part are found important for the large mixing angle. We show that the new experimental data from BaBar provide a strong constraint on the mixing angle at the mass of Ds1 (2536), from which two values can be extracted, i.e. θ1 = 32.1• or θ2 = 38.4• . Our study agrees well with the latter one. Detailed analysis of the mass shift procedure due to the coupled channel effects is also presented.