We address in this letter the learning of unknown rigid body motions in the Special Euclidian Group SE(3) based on Gaussian Processes. A new covariance kernel for SE(3) is presented and proven to be a valid kernel for Gaussian Process Regression. The learning error of the proposed Gaussian Process model is extended to a highprobability statement on SE(3). We employ it in a visual pursuit scenario of a moving target with unknown velocity in 3D space. Our approach is validated in a simulated 3D environment in Unity, and shows significant better prediction accuracy than the most commonly used Gaussian kernel. When compared to other covariance kernels proposed on SE(3), its advantages are a natural extension of covering numbers to SE(3), that it is computationally more efficient, and that stability of target pursuit can be guaranteed without limiting the target rotational space to SO(2).