Power flow exhibits uncertainty when power injections randomly fluctuate. The variables of power flow problem are correlated through the constraints set forth by power flow equations. Affine arithmetic can effectively overcome the correlation and therefore is adopted in this paper. In order to improve the computational efficiency, non-iterative method was proposed, which can transform the interval power flow problem into optimization problems. Linear programming, nonlinear programming and quadratic programming optimization models were established to obtain intervals of nodal voltage magnitude, phase angle, branch active power and reactive power, respectively. Simulation results of 9-bus and 57-bus test system show that the power flow interval obtained by the proposed algorithm is nearly the same as that by iterative algorithms, whereas the branch power flow results are better. The interval power flow problem can be solved quickly and efficiently with time complexity approximately O(m3). As well, parallel computing can be implemented to achieve promising improvement in computation time.