An intrinsic problem in domain adaptation is the joint distribution mismatch between the source and target domains. Therefore, it is crucial to match the two joint distributions such that the source domain knowledge can be properly transferred to the target domain. Unfortunately, in semi-supervised domain adaptation (SSDA) this problem still remains unsolved. In this article, we therefore present an asymmetric joint distribution matching (AJDM) approach, which seeks a couple of asymmetric matrices to linearly match the source and target joint distributions under the relative chi-square divergence. Specifically, we introduce a least square method to estimate the divergence, which is free from estimating the two joint distributions. Furthermore, we show that our AJDM approach can be generalized to a kernel version, enabling it to handle nonlinearity in the data. From the perspective of Riemannian geometry, learning the linear and nonlinear mappings are both formulated as optimization problems defined on the product of Riemannian manifolds. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed approach and testify its superiority over existing SSDA techniques.