We present the results of Suzaku observations of the galaxy cluster 1RXS J0603.3+4214 with toothbrush radio relic. Although a shock with Mach number $M simeq 4$ is expected at the outer edge of the relic from the radio observation, our temperature measurements of the intracluster medium indicate a weaker temperature difference than what is expected. The Mach number estimated from the temperature difference at the outer edge of the relic is $M simeq 1.5$, which is significantly lower than the value estimated from the radio data even considering both statistical and systematic errors. This suggests that a diffusive shock acceleration theory in the linear test particle regime, which is commonly used to link the radio spectral index to the Mach number, is invalid for this relic. We also measured the temperature difference across the western part of the relic, where a shock with $M simeq 1.6$ is suggested from the X-ray surface brightness analysis of the XMM-Newton data, and obtained consistent results in an independent way. We searched for the non-thermal inverse Compton component in the relic region and the resultant upper limit on the flux is $2.4 times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$ in the 0.3-10 keV band. The lower limit of the magnetic field strength becomes 1.6 $mu$G, which means that magnetic energy density could be more than a few $% $ of the thermal energy.
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