The present invention relates to a hydroxamic acid-based contrast agent containing an isotope of fluorine, which comprises a compound having a structure of Formula (III): wherein R1 represents radioactive fluorine-18 (18F) or isotope fluorine-19 (19F), and R2 represents hydroxyamine —(NH)OH. The hydroxamic acid-based contrast agent containing an isotope of fluorine provided in the present invention has the capability of selectively inhibiting histone deacetylase (HDAC) subtypes 8/6/3, and specifically targets to the focus of spinocerebellar ataxia with over-activation of HDAC. By labeling with the radioisotope fluorine-18, a positron emission tomography (PET) image is obtained with the hydroxamic acid-based contrast agent containing radioisotope fluorine-18, whereby spinocerebellar ataxia is effectively detected. Therefore, the hydroxamic acid-based contrast agent containing an isotope of fluorine provided in the present invention is potentially useful as a probe for early diagnosis and evaluation of the therapeutic effect of spinocerebellar ataxia.