We analytically derive quasi-normal frequencies for Kerr black hole by analytically continuing the relevant solution of Teukolsky's radial equation to the complex plane, matching the monodromy of the wave function along two different contours in the same homotopy class. Our results are in agreement with the results from WKB. We also discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies of four-dimensional Kerr black hole by expanding around the zeroth-order approximation to the wave equation.