Sensitivity analysis aims to identify which input parameters of a given mathematical model are the most important. One of the well-known sensitivity metrics is the Sobol sensitivity index. There is a number of approaches to Sobol indices estimation. In general, these approaches can be divided into two groups: Monte Carlo methods and methods based on metamodeling. Monte Carlo methods have well-established mathematical apparatus and statistical properties. However, they require a lot of model runs. Methods based on metamodeling allow to reduce a required number of model runs, but may be difficult for analysis. In this work, we focus on metamodeling approach for Sobol indices estimation, and particularly, on the initial step of this approach — design of experiments. Based on the concept of D-optimality, we propose a method for construction of an adaptive experimental design, effective for calculation of Sobol indices from a quadratic metamodel. Comparison of the proposed design of experiments with other methods is performed.