Discrete scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity which can be rarely observed in quantum systems. Here we report the log-periodic quantum oscillations in the magnetoresistance (MR) and the Hall traces of HfTe 5 crystals, which reveals the appearance of DSI. The oscillations show the same logB-periodicity in the behavior of MR and Hall, indicating an overall effect of the DSI on the transport properties. Moreover, the DSI feature in the Hall resistance signals its close relation to the carriers. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. Our work evidences the universality of the DSI in the Dirac materials and paves way for the full understanding of the novel phenomenon.Discrete scale invariance (DSI) is a partial breaking of continuous scale invariance where observables of the system obey the scale invariance only for a geometrical set of choices written as the form of n with being the scaling ratio [1]. With the violation of the classical continuous scale symmetry, the DSI represents a scale anomaly, and the characteristic signature of DSI, the intriguing log-periodicity, exists in rupture, growth processes, turbulence, finance, and so on. The appearance of log-periodic structures indicates the characteristic length scales in a system, which is extremely interesting when it is fundamentally related to the underlying physical mechanism [1].The scale anomaly DSI is of high general interest while it can be rarely observed in quantum systems experimentally [2]. For a long time, the DSI has only been confirmed in cold atom systems and generated tremendous interest [3][4][5][6][7][8][9][10]. Nowadays, the DSI behavior in Dirac materials has also attracted attention in several subfields of physics [11][12][13][14][15][16]. Especially, the magneto-transport measurements on topological material ZrTe 5 reveal a new type of