Results of a 1997 September 9-10 BeppoSAX observation of the 5.57 hr low-mass X-ray binary (LMXRB) X1822-371 are presented. The 0.3-40 keV spectrum is unusually complex and cannot be fit by any of the standard models applied to other LMXRB. At least two components are required. One component has a shape consistent with that expected from the Comptonization of an input soft (Wein) spectrum while the other, contributing ~40% of the 1-10 keV flux, is consistent with being a blackbody. In addition, there is a ``dip in the spectrum which can be modeled by a 1.33 +0.05 -0.11 keV absorption edge with an optical depth, tau, of 0.28 +/- 0.06. If the same model is fit to ASCA Solid-State Imaging Spectrometer spectra obtained in 1993 and 1996, then reasonable fits are also obtained, with a similar absorption feature required. The nature of this feature is highly uncertain; its energy corresponds to the K-edges of highly ionized Ne x and neutral Mg, or to an L-edge of moderately ionized Fe. Surprisingly, no strong (tau > 0.05) Fe-K or (tau > 0.18) O-K edges are visible. The folded lightcurve of X1822-371 is similar to previous observations, except that no strong softening is seen near the eclipse. An updated orbital ephemeris is provided.