In this paper, based on the improved complex variable least-square (ICVMLS) approximation, the improved complex variable element-free Galerkin (ICVEFG) method for two-dimensional viscoelasticity problems is proposed. The ICVMLS approximation is used to form the shape function, the Galerkin weak form is used to obtain the system equations, and the penalty method is used to impose the essential boundary conditions, then the corresponding formulae of the ICVEFG method for two-dimensional viscoelasticity problems are obtained. Finally, some numerical examples are given, and the numerical results from the ICVEFG method are compared with those from the CVEFG method and finite element method, and the results show that the ICVEFG method in this paper has the high computational precision and efficiency.