In this paper, we discuss the properties of simple modules over Auslander regular rings with global dimension at most 3. Using grade theory, we show the right projective dimension of ExtΛ1(S,Λ)$\begin{array}{} \text{Ext}_{{\it\Lambda}}^{1}(S,\ {\it\Lambda}) \end{array} $ is equal to 1 for any simple Λ-module S with gr S = 1. As a result, we give some equivalent characterization of diagonal Auslander regular rings.