The pose accuracy is a crucial issue that limits the application of hybrid robots. The model-free calibration instead of complex error modeling is investigated to improve the pose accuracy of a 5-degrees-of-freedom (DOF) hybrid robot efficiently. To overcome the difficult problem of model-free calibration in high-dimension joint space that the required measurement data for accurate prediction increase exponentially, a dimensionality reduction method is proposed to decompose high-dimension joint space into two low-dimension subspaces. Then the pose errors can be respectively measured in two subspaces based on the calibrated standard poses to train their corresponding pose error predicators. The standard poses ensure the measured pose errors in two subspaces do not affect each other. Thus, a merging operation obtained by kinematic analysis can finally merge the predicted pose errors of two subspaces into the complete pose error. The error predicators established by several regression methods including artificial neural network, extreme learning machine (ELM) and Twin Gaussian process regression are compared on multi aspects, and ELM stands out among them due to its outstanding prediction accuracy, good anti-noise ability, and low training data requirements. In addition, different representations of pose and pose error are adopted at different calibration stages to deal with the influence of parasitic motion of hybrid robot for the implementation of proposed calibration method. The compensation experiment is executed and the results show that position and orientation errors are reduced by 92.4% and 88.2% on average after calibration and the pose accuracy can meet application requirements.