Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables and these models use a non-linear function (generator) to map latent samples into the data space. On the other hand, the non-linearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. This weak projection, however, can be addressed by a Riemannian metric, and we show that geodesics computation and accurate interpolations between data samples on the Riemannian manifold can substantially improve the performance of deep generative models. In this paper, a Variational spatial-Transformer AutoEncoder (VTAE) is proposed to minimize geodesics on a Riemannian manifold and improve representation learning. In particular, we carefully design the variational autoencoder with an encoded spatial-Transformer to explicitly expand the latent variable model to data on a Riemannian manifold, and obtain global context modelling. Moreover, to have smooth and plausible interpolations while traversing between two different objects' latent representations, we propose a geodesic interpolation network different from the existing models that use linear interpolation with inferior performance. Experiments on benchmarks show that our proposed model can improve predictive accuracy and versatility over a range of computer vision tasks, including image interpolations, and reconstructions.