Electroencephalography (EEG) is a powerful technique for the study of human brain and cognitive neuroscience. Nowadays, more and more EEG data are organized in high-dimension form, which is called tensor. Tensor decomposition is just the suitable tool to exploit the multiway data and extract EEG features that are linked to cognitive processes. Since the high-dimension EEG tensor often contains a large amount of data points, highly efficient tensor decomposition algorithm is desired. In addition, EEG tensor are sometimes nonnegative and the intrinsic features usually have some special properties, such as sparse. In order to extract meaningful feature components, it is necessary to incorporate constraint and regularization to tensor decomposition algorithm. In this dissertation, we study the CANDECOMP/PARAFAC (CP) tensor decomposition with both nonnegative constraint and sparse regularization, which is abbreviated as sparse NCP. An inexact block coordinate descent (BCD) framework is employed for the non-convex sparse NCP problem. Five optimization methods are employed to solve the sparse NCP, including multiplicative update (MU), alternating nonnegative least squares/quadratic programming (ANLS/ANQP), hierarchical altering least squares (HALS), alternating proximal gradient (APG) and alternating direction method of multipliers (ADMM), all of which are carefully tailored to the sparse regularization problem. In order to improve the stability, we also utilize proximal algorithm particularly for ANLS/ANQP and HALS. Applications on real-world EEG datasets are carried out. First, we use NCP to decompose a fifth-order event-related potential (ERP) tensor, which was collected by proprioceptive stimuli on human hands. Next, ongoing EEG tensors are analyzed using sparse NCP. The data were collected by naturalistic and continuous music stimulus. Finally, we analyze two modalities of ongoing EEG tensor and music signals simultaneously by N-way partial least square (N-PLS). In conclusion, our designed tensor decomposition methods with constraint and regularization are able to decompose high-order tensor data efficiently and extract meaningful EEG features linked to cognitive processes. Keywords: Tensor decomposition, nonnegative CANDECOMP/PARAFAC, sparse regularization, block coordinate descent, EEG data analysis