Focusing on the issue that non-zero genus surface parameterization has large deformation and high computational complexity, an improved global parameterization approach based on holomorphic 1-form was proposed, which starts from the gradient field and adapts easier and faster method to compute homology and cohomology group. Firstly, a simplified cut graph method was used to construct homology group to determine the topology. Secondly, cohomology group of the linear space formed by the gradient field was calculated by defining special harmonic function to figure out closed 1-form. Thirdly, homology group was diffused to harmonic 1-form through minimizing harmonic energy. Finally, holomorphic 1-form was computed by combining linearly harmonic 1-form and the parameterization was obtained by integrating holomorphic 1-form on the surface basic domain. Theoretical analysis of homology group and cohomology group shows that the parameterization is a global, border-free conformal mapping. Experimental results based on non-zero genus model show that, compared with the former global parameterization based on holomorphic 1-form, the proposed algorithm has better visual effect, smaller average error and higher operation efficiency.