Quasi-conformal maps have bounded conformal distortion, and are the natural extension of the conformal maps. The existing techniques to compute the quasi-conformal map require a global coordinate system; thus, they are limited to models of simple topological types, such as genus-0 or 1 surfaces, for which one can obtain the global coordinates by the global parameterization. This paper presents a simple yet effective technique for computing a quasi-conformal map on surfaces of non-trivial topology. Our method extends the quasi-conformal iteration method (Lui et al., 2012) [8] from the complex plane to the manifold setting. It requires neither numerical solver nor the global coordinate system, thus, is easy to implement. Moreover, thanks to its simple and parallel structure, our method is well suited for parallel computing. Experimental results on 3D models of various topological types demonstrate the efficacy of our technique.