Summary: We present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative methods for linear systems when the coefficient matrix is either an \(H\)-matrix or a symmetric positive definite matrix. First, \(m\) parallel iterations are implemented in \(m\) different processors. Second, based on \(l_1\)-norm or \(l_2\)-norm, the \(m\) optimization models are treated in parallel in \(m\) different processors. The convergence theories are established for the parallel quasi-Chebyshev accelerated method. Finally, numerical examples show that the parallel quasi-Chebyshev technique can significantly accelerate the convergence of nonoverlapping multisplitting iterative methods.