We present a new adversarial deep learning framework for the problem of human activity recognition (HAR) using inertial sensors worn by people. Our framework incorporates a novel adversarial activity-based discrimination task that addresses inter-person variability-i.e., the fact that different people perform the same activity in different ways. Overall, our proposed framework outperforms previous approaches on three HAR datasets using a leave-one-(person)-out cross-validation (LOOCV) benchmark. Additional results demonstrate that our discrimination task yields better classification results compared to previous tasks within the same adversarial framework.