The demand for high speed data transmission has increased rapidly, leading to advanced optical communication techniques. In the past few years, multiple equalizers based on neural network (NN) have been proposed to recover signal from nonlinear distortions. However, previous experiments mainly focused on achieving low bit error rate (BER) on certain dataset with an offline-trained NN, neglecting the generalization ability of NN-based equalizer when the properties of optical link change. The development of efficient online training scheme is urgently needed. In this paper, we've proposed an adaptive online training scheme, which can fine-tune parameters of NN-based equalizer without the help of an online training sequence. By introducing data augmentation and virtual adversarial training, the convergence speed has been accelerated by 4.5 times, compared with decision-directed self-training. The proposed adaptive NN-based equalizer is called "AdaNN". Its BER has been evaluated under two scenarios: a 56 Gb/s PAM4-modulated VCSEL-MMF optical link (100-m), and a 32 Gbaud 16QAM-modulated Nyquist-WDM system (960-km SSMF). In our experiments, with the help of AdaNN, BER values can be quickly stabilized below 1e-3 after trained with 10^5 unlabeled symbols. AdaNN shows great performance improvement compared with non-adaptive NN and conventional MLSE.