The Mashhoon rotation-spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited, which results in the Minkowski metric, and the torsion axial-vector and Dirac spin coupling will give the Mashhoon rotation-spin term. For the high speed rotating cases, the tangent velocity constructed by the angular velocity $Ome$ multiplying the distance r may exceed over the speed of light c, i.e., $Ome r ge c$, which will make the relativistic factor $gamma$ infinity or imaginary. In order to avoid this meaningless difficulty occurred in $gamma$ factor, we choose to make the rotation nonuniform and position-dependent in a particular way, and then we find that the new rotation-spin coupling energy expression is consistent with the previous results in the low speed limit.
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