Various uncertainties existing in the manufacturing process, such as imperfect cable lengths and uncertain boundary node locations, will unavoidably deteriorate the shape precision of cable-network antennas. In this paper, an adaptive Kriging-based method is developed to investigate the global sensitivity of uncertain parameters and discover the influential factors. Existing strategies in literature usually use relative error of function values to measure the metamodel accuracy and then to determine when the sequential sampling process should be stopped. However, these indicators are mostly developed based on function values, not the sensitivity indices. Therefore, it is difficult to determine how small the indicators should be for efficiently defining an accurate metamodel for sensitivity analysis. In this paper, a straightforward sensitivity-based indicator is developed to measure the metamodel accuracy, which is defined as the weighted average of absolute errors of sensitivity values between two successive iterations. A use-controlled threshold, combined with the new indicator, can provide an automatic stopping criterion for the adaptive metamodel building process. The proposed method can provide a uniform framework to detect the convergence status effectively for problems with different uncertainties and dimensions. A numerical example and two cable-network antenna examples considering different manufacturing uncertainties are illustrated to validate the new method.