Abstract
We consider a nonsymmetric algebraic Riccati equation arising in transport theory. The four coefficient matrices form this equation is M-matrix, it can be determined that equation existence nonnegative solutions. We propose the new simple iterative method and Newton nonlinear black Jacobi to solve the vector equation. The convergence theorem about new simple iterative show that the sequence of vectors is monotonically increasing and converges to the minimal nonnegative solution of vector equation. Numerical experiments show that the new simple iterative is more efficient than simple iterative.