From the reduction of 2893 globally distributed astrometric and geodetic VLBI sessions from August 1979 to the end of 1998, coordinates of 722 radio sources at J2000.0, coordinates and velocities of 128 stations at J1997.0 and about 20 years Earth Orientation Parameters were estimated. From the analysis of the resultant polar motion series, the following are demonstrated: (ⅰ) During the VLBI data span the Markowitz wobble is not exhibited. (ⅱ) The amplitudes of both annual and Chandler wobble show temporal variations, with the former being more obvious than the latter. (ⅲ) Wavelet analysis shows that all the signals in the polar motion series are characterized by temporal variation in amplitudes. If we take any signal as strictly periodic, it is impossible to remove it completely from the polar motion series by least-squares fit because the hypothesis of a constant amplitude conflicts with VLBI measurements. (ⅳ) By applying a filter, the secular polar motion was found to be (2.74±0.01) mas/a towards (83.9±0.3) °W longitude, which is smaller in rate and more westward in direction compared with those determined from optical observations or the combination of optical and space geodetic observations.