One of the important challenges in designing an SSMVEP-based Brain-computer interface (BCI) under any augmented reality (AR) environment is the stability of the system under dynamically changing background conditions. In this study, a novel AR optical see-through (OST) light-weight headset was incorporated into a BCI system based on steady state-motion-visually evoked potential (SSMVEP). The AR-BCI system was evaluated in a five-class asynchronous scenario, with four intentional control (IC) states and one no-control (NC) state. The system was tested under two background conditions: active (AB) and non-active (NB) background. Offline analysis was performed to evaluate the IC vs. NC classification performance using the complex-spectrum based convolutional neural network (C-CNN). The average performance metrics for 1-second window length were (NB vs. AB): Accuracy: 83%±9% vs. 81%±8%, F1-score: 0.82±0.1 vs. 0.80±0.09 and False Activation Rate: 16%±11% vs. 17%±10%. The results suggested that the C-CNN method applied on the SSMVEP responses in AR provides high IC vs. NC classification performance, and more importantly, is robust to change in dynamically changing background conditions.