A lower-limb exoskeleton robot identifies the wearer's walking intention and assists the walking movement through mechanical force; thus, it is important to be able to identify the wearer's movement in real-time. Measurement of the angle of the knee and ankle can be difficult in the case of patients who cannot move the lower-limb joint properly. Therefore, in this study, the knee angle as well as the angles of the talocrural and subtalar joints of the ankle were estimated during walking by applying the neural network to two inertial measurement unit (IMU) sensors attached to the thigh and shank. First, for angle estimation, the gyroscope and accelerometer data of the IMU sensor were obtained while walking at a treadmill speed of 1 to 2.5 km/h while wearing an exoskeleton robot. The weights according to each walking speed were calculated using a neural network algorithm programmed in MATLAB software. Second, an appropriate weight was selected according to the walking speed through the IMU data, and the knee angle and the angles of the talocrural and subtalar joints of the ankle were estimated in real-time during walking through a feedforward neural network using the IMU data received in real-time. We confirmed that the angle estimation error was accurately estimated as 1.69° ± 1.43 (mean absolute error (MAE) ± standard deviation (SD)) for the knee joint, 1.29° ± 1.01 for the talocrural joint, and 0.82° ± 0.69 for the subtalar joint. Therefore, the proposed algorithm has potential for gait rehabilitation as it addresses the difficulty of estimating angles of lower extremity patients using torque and EMG sensors.