A stable high-intensity atomic beam source plays a key role in many precision measurements. The precision spectroscopy of slow metastable (2^3\rm S) helium atoms is of great interest in testing quantum electrodynamics and determining the fine structure constant. By improving the source cavity structure and using laser cooling method, the beam flux is greatly enhanced. The added Zeeman slower reduces the longitudinal velocity of atoms, and at the same time increases the beam brightness of atoms at one single speed. Near the back end of Zeeman slower, a two-dimensional magneto-optical trap is added to collimate and focus the atomic beam. In addition, A beam stabilizing system is developed by using feedback control method. By changing the frequency of transverse cooling laser to change the cooling efficiency, the fluctuation of atomic beam intensity can be compensated in real time, and then the beam intensity can be stabilized at the target number. Experiments show that the continuous beam of metastable helium atoms at a velocity of (100\pm 3.6) m/s has an intensity of 5.8\times10^12 atoms/s/sr and a relative stability of 0.021%. In the experiment of precise spectral measurement based on atomic beam, the narrow longitudinal velocity distribution reduces the lateral Doppler broadening effect, and the lower longitudinal velocity also reasonably reduces the systematic error caused by the first-order Doppler effect. The atomic beam with such high intensity and stability in a single momentum and quantum state obviously improves the signal-to-noise ratio of the spectrum, and further reduces the statistical error of the results in the same detection time. Using this atomic beam, we demonstrated spectroscopy of the 2^3\rm S-2^3\rm P transition of ^4\rmHe under the condition of only 0.1% of the saturated intensity. At this time, the full width at half maximum of the spectral peak is almost close to the natural line width, but the spectral signal-to-noise ratio is still better than 400 and the frequency shift caused by the detection laser power can be less than 1 kHz. This kind of spectral detection at low power can effectively reduce the power-dependent frequency shift, thus obtaining more reliable detection results. This metastable helium atom beam experimental system can also be used as a reference for similar precision measurement experiments.