A high-precision straightening machine for a tantalum niobium alloy pipe comprises a straightening main machine, a hydraulic servo system and an electrical control system, wherein the straightening main machine adopts a structure of 2-2(12) compound roll and is provided with six pairs of straightening rolls which are symmetrically arranged up and down; a first pair, a second pair and a third pair of rolls are big rolls and a fourth pair, a fifth pair and a sixth pair of rolls are small rolls; each straightening roll has a sectional, equal-curvature and back-bending shape; the roll distances of the straightening rolls are different; and the hydraulic servo system and the electrical control system perform closed loop control on the displacements of the straightening rolls and the pressure of the straightening main machine and perform stepless regulation on the straightening speed. By using the straightening machine, the diameter ratio of a straightened material can reach 1to 5, the diameter Phi of the straightened material is 15 to 70mm, the wall thickness of the straightened material is 0.245 to 0.381mm, and the straightening precision can reach 0.3mm/m; and the straightening machine can straighten pipes made of high-strength alloy materials such as a high-quality alloy steel and the like.