We improve High Dynamic Range (HDR) Image Quality Assessment (IQA) using a full reference approach that combines results from various quality metrics (HDR-CQM). We combine metrics designed for different applications such as HDR, SDR and color difference measures in a single unifying framework using simple linear regression techniques and other non-linear machine learning (ML) based approaches. We find that using a non-linear combination of scores from different quality metrics using support vector machine is better at prediction than the other techniques such as random forest, random trees, multilayer perceptron or a radial basis function network. To improve performance and reduce complexity of the proposed approach, we use the Sequential Floating Selection technique to select a subset of metrics from a list of quality metrics. We evaluate the performance on two publicly available calibrated databases with different types of distortion and demonstrate improved performance using HDR-CQM as compared to several existing IQA metrics. We also show the generality and robustness of our approach using cross-database evaluation.