AbstractIn this article, we establish a Lyapunov-type inequality for the following extremal Pucci’s equation:$$\begin{eqnarray}\left\{\begin{array}{@{}ll@{}}{\mathcal{M}}_{\unicode[STIX]{x1D706},\unicode[STIX]{x1D6EC}}^{+}(D^{2}u)+b(x)|Du|+a(x)u=0 & \text{in}~\unicode[STIX]{x1D6FA},\\ u=0 & \text{on}~\unicode[STIX]{x2202}\unicode[STIX]{x1D6FA},\end{array}\right.\end{eqnarray}$$where$\unicode[STIX]{x1D6FA}$is a smooth bounded domain in$\mathbb{R}^{N}$,$N\geq 2$. This work generalizes the well-known works on the Lyapunov inequality for extremal Pucci’s equations with gradient nonlinearity.