Due to the recent technological development, home appliances and electric devices are equipped with high-performance hardware device. Since demand of hardware devices is increased, production base become internationalized to mass-produce hardware devices with low cost and hardware vendors outsource their products to third-party vendors. Accordingly, malicious third-party vendors can easily insert malfunctions (also known as 'hardware Trojans') into their products. In this paper, we design six kinds of hardware Trojans at a gate-level netlist, and apply a neural-network (NN) based hardware-Trojan detection method to them. The designed hardware Trojans are different in trigger circuits. In addition, we insert them to normal circuits, and detect hardware Trojans using a machine-learning-based hardware-Trojan detection method with neural networks. In our experiment, we learned Trojan-infected benchmarks using NN, and performed cross validation to evaluate the learned NN. The experimental results demonstrate that the average TPR (True Positive Rate) becomes 72.9%, the average TNR (True Negative Rate) becomes 90.0%.