High-precision timing observations of the millisecond pulsar PSR B1821-24 have been conducted at the Nancay radiotelescope between 1.37GHz and 1.7GHz since January 22, 1992 until January 10, 1996. This dense and precise multi-frequency timing series has allowed secular variations of the dispersion measure as high as 0.005pc/cm^3^/year in the direction of this pulsar to be determined. The index β of the power-law spatial spectrum of the electron density fluctuations has been determined for the first time in the direction of this pulsar and is 3.727+/-0.211, a result consistent with a Kolmogorov turbulent medium. The diffractive time scale τ_d_ is also determined to be 50+/-_ 40_^183^ s and is relatively consistent with the determination based on the space velocity of PSR B1821-24. We also provide a new proper motion for this pulsar for which the declination component is for the first time inconsistent with zero.