Electron cooling method is used for the High Intensity heavy-ion Accelerator Facility (HIAF), in order to reduce the beam emittance and momentum spread of heavy ion beams, hence to improve the accuracy and luminosity of nuclear physics and atomic physics experiments. The magnetic field homogeneity of the cooling section is the key parameter related to the cooling effect. A new type of cooling section solenoid composed of several coils was used in the HIAF electron cooling device to produce a high parallelism magnetic field. In this paper, a device for the magnetic field axis measurement of high-precision coils is presented. The geometric symmetrical axis of the coil is measured by a positioning device. The radial and axial magnetic field distribution in the center plane of the coil is measured by the rotating Hall probes. Finally, the relative angle between the coil magnetic field axis and the geometric symmetrical axis is calculated by the measurement results. The accuracy of the measured angle is within ±0.10 mrad. The measured angle of the prototype coil is (1.28±0.10) mrad, which satisfies the physics requirement.