Motion estimation from cardiac image is a very important technique to study the architecture and function of heart. However quantitative motion analysis from cardiac images is still a challenging problem due to the complexity of cardiac motion and limitations in spatial and temporal image resolutions. We develop a robust temporally consistent diffeomorphic motion estimation algorithm based on mutual information similarity measurement. It extends the current large deformation diffeomorphic registration method by the usage of statistical similarity measurement. In our algorithm, the spatial transformation is parameterized by a smooth velocity field with a transport equation. The optimal velocity field is obtained by minimizing a geodesic path on the diffeomorphic transformation manifold and simultaneously minimizing the frame to frame negative mutual information. The Euler-Lagrange equation of the variational functional is derived and the numerical method based on 3D+t B-spline is proposed. Our method is applied to the simulated and real 3D+t echocardiographic sequences. Experimental results show the improvements of our method over the diffeomorphic method using the sum of squared difference similarity metric.