Tensor data, characterized as multi-dimensional arrays, have been increasingly prevalent in biomedical studies, e.g., in neuroimaging applications. The tensor regression is challenging due to the high-dimensionality and complex spatial structure of tensor data. The regression of average responses on tensor predictors has been well investigated, but there is limited literature on the quantile regression with tensor predictors, which fulfills the keen practical interest in the non-average responses and robust inference. The existing quantile tensor regression methods are computationally heavy and yield a non-unique tensor estimator structure. We develop a computationally efficient approach for quantile tensor regression under the envelope concept. The envelope model allows the unique construction of the tensor estimators. We show that the estimators are root-n consistent under mild conditions. Simulation studies illustrate that the bias of the proposed estimators is negligible even under a small sample and outperforms existing methods. We apply our method to investigate the association between PTSD clinical symptoms and brain connectivity matrices in a mental health study.