  We show that the arithmetic D-module associated to an overconvergent
F-isocrystal over a smooth curve is holonomic. We first prove that unipotent
F-isocrystals are holonomic D-module by using the fact that such F-isocrystals
come from logarithmic F-isocrystals. We deduce the general case from the
semi-stable theorem for F-isocrystals over curves of Matsuda-Trihan which
relies on the p-adic monodromy theorem independently proved by Andr\'e, Kedlaya
and Mebkhout. The main result has already been proved by D. Caro.
