This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI), and a large number of subjects. Unlink previous methods, DHA is not limited by a restricted fixed kernel function. Further, it uses a parametric approach, rank-m Singular Value Decomposition (SVD), and stochastic gradient descent for optimization. Consequently, the time complexity of DHA fairly scales with data size and the training data is not referenced when DHA computes the functional alignment for a new subject. Experimental studies on multi-subject fMRI analysis confirm that the DHA method achieves superior performance to other state-of-the-art HA algorithms.