The fundamental properties of electron relativistic radial wave functions have been studied theoretically based on the relativistic average self - consistent field. Usually，the small - component of relativistic radial wave functions is several orders of magnitudes less than the large - component，and is not generally synchronous with the large - component，so the radial probability density of electron has no exact zeros. The number of nodes for bound electron large - or small - component is n - l - 1，so that the number of antinodes is n - l，but the number of nodes and antinodes for free electron just turn to infinite. The radial wave functions are extremely sensitive to the relativistic effects，the amplitude of small - component increases with increasing relativistic effects，as well as the oscillating intensity of large，small - component for free electron.