Quantitative motion analysis from cardiac imaging is an important yet challenging problem. Most of the existing cardiac motion estimation methods ignore the fact that the myocardium is a fibrous structure with elastic anisotropy. We propose a novel method in which an anisotropic regularization energy is used to favor the motion consistency with the myofiber orientation. The myofiber direction comes from a diffusion tensor image and it is mapped to the end-diastole frame by using nonrigid registration. We implement the method based on a diffeomorphic motion estimation framework in which a spatiotemporally smooth velocity field is estimated by optimization of a variational energy. We validate the proposed method by using cine magnetic resonance imaging (MRI) datasets and echocardiography of an open-chest pig with sonomicrometry. We compare the proposed method with a temporal diffeomorphic free form deformation method without consideration of myofiber orientation. Experiments results show that the proposed motion estimation method has higher accuracy.