In this work is presented new algorithm, called Truncated Hierarchical SVD (THSVD), aimed at the processing of sequences of correlated images, represented as third-order tensors. The algorithm is based on the multiple calculation of the matrix SVD for elementary tensors (ET) of size 2×2×2, which build the tensor of size N×N×N, when N=2n. The new approach is compared to closest famous hierarchical SVD methods for ET: the Sequential Unfolding SVD (SUSVD) and the Radix 2×2Hierarchical SVD (Radix 2×2 HSVD). New two-level algorithm is developed for ET decomposition, with lower computational complexity than these of Radix 2×2 HSVD and SUSVD. In the paper is presented the THSVD algorithm for tensor of size 4×4×4, which is generalized for a tensor of size N×N×N. Adaptive new algorithm is offered for the “truncation” of the tensor decomposition components with small weights. The multiple execution of similar operations for the SVD calculation for matrices of size 2×2 in each THSVD level, permits its parallel implementation by using processors with relatively simple structures. As a result of the „truncation“ and of the parallel calculations of THSVD, the processing of image sequences represented by third-order tensors, is significantly accelerated. This advantage of the algorithm opens new abilities for its application in real-time image processing systems in various areas: compression of image sequences, digital watermarking, computer vision, machine learning, processing of multidimensional signals, etc.