Let $\Omega$ be an open subset in ${\bf R}^n \; (n \geq 3)$. In this paper, we study the partial regularity for stationary positive weak solutions of the equation $$\Delta u+h_1 (x) u+h_2 (x) u^\alpha=0 \;\;\;\;\; \mbox{in} \;\; \Omega .\leqno(1.1)$$ We prove that if $\alpha>\frac{n+2}{n-2}$, and $u \in H^1(\Omega) \cap L^{\alpha+1} (\Omega)$ is a stationary positive weak solution of (1.1), then the Hausdorff dimension of the singular set of $u$ is less than $n-2 \frac{\alpha+1}{\alpha-1}$, which generalizes the main results in Pacard 1993 and Pacard 1994.