Background: Faithful and accurate and successful cardiac biomechanics simulations require patient-specific geometric models of the heart. Such simulations can be performed using high-order partial differential equation solvers, such as finite element methods. Since cardiac geometry consists of highly-curved boundaries, the use of high-order meshes that consist of both curved and straight elements would ensure that the various curves and features present in the cardiac geometry are preserved and well-captured in the corresponding mesh. Moreover, high-order partial differential equation solvers will yield more accurate solutions when paired with high-order meshes. Methods: Here we propose a novel, direct method for generating high-order curvilinear tetrahedral meshes from clinical quality medical images using an advancing front approach. Our method takes a high-order surface mesh as input and generates a high-order volume mesh directly from that curved surface mesh. We employ our method to generate several second-order meshes of cardiac boundary representations for various left ventricle myocardia obtained from magnetic resonance images (MRI). Results: We use scaled Jacobian and equiangular skewness to assess the quality of our meshes. Acceptable scaled Jacobian values range from -∞ to 1, with values near 1 indicating the best quality. Equiangular skewness ranges from 0 to 1, where values closest to 0 indicate the best quality. The minimum scaled Jacobian for our meshes ranges from 0.106-0.123, whereas the maximum equiangular skewness values range from 0.879-0.919. Furthermore, our high-order cardiac meshes do not contain inverted elements and feature the high quality necessary for use in finite element simulations. Conclusion: Our method yields high-quality mesh elements at the time of mesh generation with minimal post-processing. We will extend our method to generate cardiac meshes that include additional features, such as the cardiac fiber architecture along with the myocardium, and demonstrate the mesh use for various cardiac biomechanics simulations.