Relativistic temperature of gas raises the issue of the equation of state (EOS) in relativistic hydrodynamics. We study the EOS for numerical relativistic hydrodynamics, and propose a new EOS that is simple and yet approximates very closely the EOS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EOSs considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EOS, in a way that they can be used to build numerical codes. Tests with a code based on the total variation diminishing (TVD) scheme are presented to highlight the differences induced by different EOSs.
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