Clusters of galaxies are believed to grow through gas accretion from large-scale filaments and mergers of smaller clusters and galaxy groups. In this process of hierarchical growth, major cluster mergers have a significant effect on the internal structure of clusters as 10^63−64 ergs of gravitational energy is converted to thermal energy, driving large shocks and turbulence. The first clear example of a merger induced shock front was found in the Bullet cluster using Chandra (Markevitch+ 2002). Recently, radio observations have revealed arc-like structures in the outskirts of merging clusters, so-called "radio relics" (e.g., Ferrari+ 2012). The synchrotron emission from radio relics is believed to come from relativistic electrons, accelerated by a shock in the intracluster medium (ICM). We will present the results of Suzaku X-ray observations of radio relic clusters. In our samples, we found that the temperature and pressure of ICM show significant drops across the radio relics, suggesting the existence of shock fronts at radio relics. The derived Mach numbers based on Rankine-Hugoniot jump condition span the range of 2-3 (Akamatsu & Kawahara 2013). Importantly, combination of X-ray and Radio observations shed new insight on poorly understood process of particle acceleration at low-Mach number (M < 5) shocks. We will discuss recent progress of our understanding of the particle acceleration in clusters of galaxies.