Linear algebra algorithms, such as the Householder QR decomposition, are pivotal in various applications including signal processing, optimization, and numerical solutions to systems of linear equations. Traditional sequential implementations of the Householder algorithm face significant limitations in terms of performance and scalability when applied to large matrices. To overcome these constraints, this paper explores the parallelization of the Householder QR algorithm on Graphics Processing Units (GPUs) using CUDA, a parallel computing platform and programming model developed by NVIDIA. Our method ensures the availability of critical intermediate data, distinguishing it from standard libraries like cuSOLVER, which modify the processing order and often discard important intermediate computations. By leveraging CUDA streams, we achieve enhanced parallelism without compromising the integrity of the algorithm’s sequence or the accessibility of intermediate data. Our performance analysis reveals that our implementation achieves efficiency comparable to cuSOLVER, making it a viable option. This study not only presents a novel implementation but also extends the potential for GPU-accelerated linear algebra procedures to benefit a wider range of scientific and engineering applications.