The aim of this presentation is to detail a state-space representation of the simple GR4J model. The state-space representation aims to represent GR4J by an ODE system which provides the internal variables of the model at all times. We will present here the choices made to adapt GR4J to the state-space formulation and to numerically solve this system. Modifications of the model’s equations were also made to adapt the model to lower time step in case it would be used for a time step-variable application.