To minimize the straightness error of deflected Longitudinally Submerged Arc Welding (LSAW) pipes, a quantitative control strategy of pressure straightening process with multi-step three-point bending is studied. Based on the springback equation of small curvature plane bending and the equivalent principle for over-bend straightening, this paper proposes a theoretical straightening moment which corresponds with the initial deflection distribution of pipes. The principle of the multi-step pressure straightening process is revealed, and the parameters in three-point bending process for each step can be obtained only by measuring the initial deflection distribution once. To improve the straightening efficiency and ensure the straightening accuracy, the concept of load correction coefficient is firstly proposed. Experimental results show that when the number of straightening step is fixed, the residual deflection of the pipe is reduced with the growth of load correction coefficient. Meanwhile, as the number of straightening step increases, the load correction coefficient decreases. The feasibility and the reliability of the control strategy are verified by the physical simulation experiments of small pipes.