Semi-supervised learning (SSL) methods, which can leverage a large amount of unlabeled data for improved performance, has attracted increasing attention recently. In this paper, we introduce a novel Context-aware Conditional Cross Pseudo Supervision method (referred as C$^3$PS) for semi-supervised medical image segmentation. Unlike previously published Cross Pseudo Supervision (CPS) works, this paper introduces a novel Conditional Cross Pseudo Supervision (CCPS) mechanism where the cross pseudo supervision is conditioned on a given class label. Context-awareness is further introduced in the CCPS to improve the quality of pseudo-labels for cross pseudo supervision. The proposed method has the additional advantage that in the later training stage, it can focus on the learning of hard organs. Validated on two typical yet challenging medical image segmentation tasks, our method demonstrates superior performance over the state-of-the-art methods.