One of the major challenges in acoustic modelling of child speech is the rapid changes that occur in the children's articulators as they grow up, their differing growth rates and the subsequent high variability in the same age group. These high acoustic variations along with the scarcity of child speech corpora have impeded the development of a reliable speech recognition system for children. In this paper, a speaker- and age-invariant training approach based on adversarial multi-task learning is proposed. The system consists of one generator shared network that learns to generate speaker- and age-invariant features connected to three discrimination networks, for phoneme, age, and speaker. The generator network is trained to minimize the phoneme-discrimination loss and maximize the speaker- and age-discrimination losses in an adversarial multi-task learning fashion. The generator network is a Time Delay Neural Network (TDNN) architecture while the three discriminators are feed-forward networks. The system was applied to the OGI speech corpora and achieved a 13% reduction in the WER of the ASR.