This paper focuses on the Hölder continuity and the Box Dimension to the [Formula: see text]th Hadamard Fractional Integral (HFI) on a given interval [Formula: see text]. We use [Formula: see text] to denote it. In this paper, two different methods are used to study this problem. By using the approximation method, we obtain that for [Formula: see text] with [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text] is [Formula: see text]th Hölder continuous in [Formula: see text] with [Formula: see text], and is [Formula: see text]th Hölder continuous on [Formula: see text]. Moreover, the Box Dimension of the graph of [Formula: see text] on the interval [Formula: see text] is less than or equal to [Formula: see text]. If [Formula: see text], then [Formula: see text] is locally [Formula: see text]th Hölder continuous in [Formula: see text] with the same [Formula: see text], and the Box Dimension of [Formula: see text] on [Formula: see text] is less than or equal to [Formula: see text]. By using another method, we imply that, for [Formula: see text] with [Formula: see text] and [Formula: see text], if [Formula: see text], then [Formula: see text] is [Formula: see text]th Hölder continuous, and thus the Box Dimension of the graph of [Formula: see text] is no more than [Formula: see text]; if [Formula: see text], then [Formula: see text] is locally [Formula: see text]th Hölder continuous in [Formula: see text], and is [Formula: see text]th Hölder continuous at [Formula: see text]. Then the Box Dimension of the graph to [Formula: see text] on [Formula: see text] is less than or equal to [Formula: see text]. We also give two examples to show that the above Hölder indexes given by the second method are optimal.