SummaryThis paper focuses on the global ‐stability of the nonlinear positive system with multiple time‐varying delays. Through differentiated expressions of the function , the global ‐stability could be referred to as several known stabilities, including Lagrange stability, asymptotic stability, global exponential stability, global practical stability, and so forth. By proposing a direct analysis method that differs from the so‐called Lyapunov‐Krasovskii functional method, we presented a sufficient condition for the global ‐stability of such system. The obtained stability condition appeared in the form of a number of simple inequalities, which could be easily handled by the toolbox YALMIP loaded in MATLAB. The applicability of our results have been illustrated by three numerical examples.