Low temperature specific heat has been measured in superconductor $beta$-FeS with T$_c$ = 4.55 K. It is found that the low temperature electronic specific heat C$_e$/T can be fitted to a linear relation in the low temperature region, but fails to be described by an exponential relation as expected by an s-wave gap. We try fittings to the data with different gap structures and find that a model with one or two nodal gaps can fit the data. Under a magnetic field, the field induced specific heat $Deltagamma$=[C$_e$(H)-C$_e$(0)]/T shows the Volovik relation $Deltagamma_e(H)propto sqrt{H}$, suggesting the presence of nodal gap(s) in this material.
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