A clamping apparatus of a puller includes a first clamping element, two second clamping elements, four pivoting elements and three adjusting rod modules. Each pivoting element is pivotally coupled to both ends of the first clamping element and an end of each second clamping element corresponding to the first clamping element. Another end of each second clamping element has a transverse penetrating hole. One of the adjusting rod modules is passed through a penetrating hole of each second clamping element, and the other two adjusting rod modules are passed through the penetrating hole of each pivoting element, so that the adjusting rod modules are arranged substantially in a triangular shape. The pivoting element is installed between the clamping elements for pivotally turning each adjusting rod module and automatically guiding to the central position and increasing the range between the clamping elements for mounting and installing a bearing easily.