In this work, a theoretical method, taking into account the anisotropy of the internal magnetic field (_int), is proposed to predict the rate of quantum tunneling of magnetization (QTM), i.e., τ_QTM⁻¹, for Kramers single-ion magnets (SIMs). Direct comparison to both experimental and previous theoretical results of three typical Kramers SIMs indicates the necessity of the inclusion of the anisotropy of _int for accurate description of QTM. The predictions of the method here are consistent with the theory proposed by Prokof'ev and Stamp (PS). For Kramers SIMs of high magnetic axiality, the QTM rates, predicted by the method here, are almost linearly proportional to the results by the PS method. The dependence of τ_QTM⁻¹ on various parameters is analyzed for model systems. The averaged magnitude of _int (B_ave) and principal g value of the axial direction (g_Z) are the parameters on which τ_QTM⁻¹ is linearly dependent. The ones on which τ_QTM⁻¹ is quadratically dependent are g_XY, i.e., the principal g value of the transversal direction, and x_aniso characterizing the anisotropy of _int. Compared to B_ave and g_Z, g_XY and x_aniso provide a higher order of dependence for QTM. Therefore regulation of the SMM property via introduction of desired values of g_XY and x_aniso ought to be a strategy more efficient than the one via B_ave and g_Z. Being different from the one via g_XY, the strategy via x_aniso to regulate the QTM has been rarely touched upon according to our best knowledge. However, this strategy could also lead to significant improvement since it is the same as g_XY in the aspect of the dependence of τ_QTM⁻¹.