In this paper, starting from the relation between the Anderson-Grüneisen parameter δ (T,P) and the second Grüneisen parameter q, we obtain a new computing formula for the volume and pressure dependence of the Grüneisen parameter γ at high temperature. Applying this formula to sodium chloride, lithium, sodium, and potassium in different pressure ranges, we find that the calculated values of the Grüneisen parameter γ are in good agreement with the experimental values.