This article investigates the input-to-state consensus (ISC) of nonlinear positive multi-agent systems (MAS). Firstly, using the max-separable input-to-state stability (ISS) Lyapunov function method, some sufficient conditions are given for the ISC of nonlinear positive MAS under state feedback and impulsive control. Based on these conditions, the multi-agent systems with a non-negative constant leader is considered, and then some sufficient conditions are also obtained for the ISC of the MAS under state feedback and impulsive control. Simulation examples verify the effectiveness of our results.