Kinship verification aims to determine whether two given persons are blood relatives. This technique can be leveraged in many real-world scenarios, such as finding missing people, identification of kinship in forensic medicine, and certain types of interdisciplinary research. Most existing methods extract facial features directly from given images and examine the full set of features to verify kinship. However, most approaches are easily affected by the age gap among faces, with few methods taking age into account. This paper accordingly proposes an Age-Invariant Adversarial Feature learning module (AIAF), which is capable of factoring in full facial features to create two uncorrelated components, i.e., identity-related features and age-related features. More specifically, we harness a type of adversarial mechanism to make the correlation between these two components as small as possible. Moreover, to pay different attention to identity-related features, we present an Identity Feature Weighted module (IFW). Only purified identity features are fed into the IFW module, which can assign different weights to the features according to their importance in the kinship verification task. Experimental results on three public popular datasets demonstrate that our approach is able to capture useful age-invariant features, i.e., identity features, and achieve significant improvements compared with other state-of-the-art methods on both small-scale and large-scale datasets.