  The purpose of this paper is to classify Anosov flows on the 3-manifolds
obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is
denoted by M(r) (r is a ratioanl number), which contains the first class of
hyperbolic 3-manifolds admitting Anosov flows in history, discovered by
Goodman. Combining with the classification of Anosov flows on the sol-manifold
M(0) due to Plante, we have: 1. if r is an integer, up to topological
equivalence, M(r) exactly carries a unique Anosov flow, which is constructed by
Goodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov flow; 2.
if r is not an integer, M(r) does not carry any Anosov flow. As a consequence
of the second result, we get infinitely many closed orientable hyperbolic
3-manifolds which carry taut foliations but does not carry any Anosov flow. The
fundamental tool in the proofs is the set of branched surfaces built by
Schwider, which is used to carry essential laminations on M(r).
