Despite the vast literature on Human Activity Recognition (HAR) with wearable inertial sensor data, it is perhaps surprising that there are few studies investigating semisupervised learning for HAR, particularly in a challenging scenario with class imbalance problem. In this work, we present a new benchmark, called A*HAR, towards semisupervised learning for class-imbalanced HAR. We evaluate state-of-the-art semi-supervised learning method on A*HAR, by combining Mean Teacher and Convolutional Neural Network. Interestingly, we find that Mean Teacher boosts the overall performance when training the classifier with fewer labelled samples and a large amount of unlabeled samples, but the classifier falls short in handling unbalanced activities. These findings lead to an interesting open problem, i.e., development of semi-supervised HAR algorithms that are class-imbalance aware without any prior knowledge on the class distribution for unlabeled samples. The dataset and benchmark evaluation are released at https://github.com/I2RDL2/ASTAR-HAR for future research.