We investigate the K1--> K pi pi strong interaction decays. Using the 3P0 quark-pair-creation model to derive the basic parametrization, we discuss in detail how to obtain the various partial wave amplitudes into the possible quasi-two-body decay channels as well as their relative phases from the currently available experimental data. We obtain the K1 mixing angle to be thetaK1= 60 deg, in agreement with previous works. Our study can be applied to extract the information needed for the photon polarization determination of the radiative B--> K1 gamma decay.