Gaussian Mixture Models (GMMs) are widely used in many applications such as data mining, signal processing and computer vision, for probability density modeling and soft clustering. However, the parameters of a GMM need to be estimated from data by, for example, the Expectation-Maximization algorithm for Gaussian Mixture Models (EM-GMM), which is computationally demanding. This paper presents a novel design for the EM-GMM algorithm targeting reconfigurable platforms, with five main contributions. First, a pipeline-friendly EM-GMM with diagonal covariance matrices that can easily be mapped to hardware architectures. Second, a function evaluation unit for Gaussian probability density based on fixed-point arithmetic. Third, our approach is extended to support a wide range of dimensions or/and components by fitting multiple pieces of smaller dimensions onto an FPGA chip. Fourth, we derive a cost and performance model that estimates logic resources. Fifth, our dataflow design targeting the Maxeler MPC-X2000 with a Stratix-5SGSD8 FPGA can run over 200 times faster than a 6-core Xeon E5645 processor, and over 39 times faster than a Pascal TITAN-X GPU. Our design provides a practical solution to applications for training and explores better parameters for GMMs with hundreds of millions of high dimensional input instances, for low-latency and high-performance applications.