The mixing mechanism of axial-vectors D-s1(2460) and D-s1(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 root s = 2454.5 MeV corresponding to D-s1(2460) and the other at root s = (2544.9 - 1.0i) MeV corresponding to D-s1(2536). For D-s1(2460), a large mixing angle theta = 47.5 degrees between P-3(1) and P-1(1) is obtained. It is driven by the real part of the mixing matrix element and corresponds to theta' = 12.3 degrees between the j = 1/2 and j = 3/2 state mixing in the heavy quark limit. For D-s1(2536), a mixing angle theta = 39.7 degrees, which corresponds to theta' = 4.4 degrees in the heavy quark limit, is found. An additional phase angle phi = -6.9 degrees similar to 6.9 degrees is needed at the pole mass of D-s1(2536) since the mixing matrix elements are complex numbers. Both the real and imaginary parts 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 D-s1(2536), from which two values can be extracted, i.e., theta(1) = 32.1 degrees or theta(2) = 38.4 degrees. Our study agrees well with the latter one. Detailed analysis of the mass-shift procedure due to the coupled channel effects is also presented.