The present invention provides a method and apparatus for QR-factorizing matrix on a multiprocessor system, wherein the multiprocessor system comprises at least one core processor and a plurality of accelerators, the method comprises the steps of: iteratively factorizing each panel in the matrix until the whole matrix is factorized; wherein in each iteration, the method comprises: partitioning an unprocessed matrix part in the matrix into a plurality of blocks according to a predetermined block size; partitioning a current processed panel in the unprocessed matrix part into at least two sub panels, wherein the current processed panel is composed of a plurality of blocks; and performing QR factorization one by one on the at least two sub panels with the plurality of accelerators, and updating the data of the sub panel(s) on which no QR factorization has been performed among the at least two sub panels by using the factorization result. The present invention enables a multiprocessor system having a high computing capability to be applied to the matrix QR factorization having a large amount of computation tasks.