The stability of intense electron beam via the periodic static electric and magnetic fields is discussed. The stability and instability regions of cylindrical electron beam through periodic harmonic electromagnetic field and periodic anharmonic fields in sawtooth, square, and trapezoid forms are given. Compared with the major instability regions of the various fields, the instability region of the saw-tooth form is smaller than others.When space charge effect is appreciable, the electron beam in the stable region is conditionally rather than unconditionally stable. It is dependent on the intensity of the space-charge current and the amplitude of the eletron beam.