Domain adaptation aims to learn an adaptive classifier for target data using the labelled source data from a different distribution. Most proposed works construct cross-domain classifier by exploring one-sided property of the input data, i.e., either geometric or statistical property. Therefore they may ignore the complementarity between the two properties. Moreover, many previous methods implement knowledge transfer with two separated steps: divergence minimization and classifier construction, which degrades the adaptation robustness. In order to address such problems, we propose a unified cross-domain classification method via geometric and statistical adaptations (UCGS). UCGS models the divergence minimization and classifier construction in a unified way based on structural risk minimization principle and coupled adaptations theory. Specifically, UCGS constructs an adaptive model by simultaneously minimizing the structural risk on labelled source data, using Maximum Mean Discrepancy (MMD) criterion to implement statistical adaptation, and flexibly employing the Nyström method to explore the geometric connections between domains. A domain-invariant graph is successfully constructed to link the two domains geometrically. The standard supervised methods can be used to instantiate UCGS to handle inter-domain classification problems. Comprehensive experiments show the superiority of UCGS on several real-world datasets.