Digital predistorsion (DPD) is a commonly used approach to compensate for the power amplifiers (PA) nonlinearities and memory effects as well as to improve its power efficiency. To alleviate the restriction brought by high peak-to-average power ratio (PAPR) of input signals, crest factor reduction (CFR) is needed for higher efficiency. In modern communication systems, power of transmitted signals gets lower, which makes complexities of CFR and DPD become non-negligible. This paper proposes a new approach to realize a joint CFR and DPD model using neural networks (NN). The modeling accuracy is guaranteed by a new proposed augmented iterative learning control (AILC) algorithm for the NN training signals. Compared with conventional ILC, the proposed AILC is shown more robust according to simulation and experimental results. The proposed AILC-based NN-CFRDPD is experimentally evaluated on different test benches.