In recent years, analyzing task-based fMRI (tfMRI) data has become an essential tool for understanding brain function and networks. However, due to the sheer size of tfMRI data, its intrinsic complex structure, and lack of ground truth of underlying neural activities, modeling tfMRI data is hard and challenging. Previously proposed data modeling methods including Independent Component Analysis (ICA) and Sparse Dictionary Learning only provided shallow models based on blind source separation under the strong assumption that original fMRI signals could be linearly decomposed into time series components with corresponding spatial maps. Given the Convolutional Neural Network (CNN) successes in learning hierarchical abstractions from low-level data such as tfMRI time series, in this work we propose a novel scalable distributed deep CNN autoencoder model and apply it for fMRI big data analysis. This model aims to both learn the complex hierarchical structures of the tfMRI big data and to leverage the processing power of multiple GPUs in a distributed fashion. To deploy such a model, we have created an enhanced processing pipeline on the top of Apache Spark and Tensorflow, leveraging from a large cluster of GPU nodes over cloud. Experimental results from applying the model on the Human Connectome Project (HCP) data show that the proposed model is efficient and scalable toward tfMRI big data modeling and analytics, thus enabling data-driven extraction of hierarchical neuroscientific information from massive fMRI big data.