We propose in this article a continuous approach to model functional-structural plant growth based on the discrete GreenLab model. The continuous dynamics is driven by a system of differential equations with respect to calendar time, with a continuous mechanism of senescence introducing delay terms. A numerical scheme for solving the system is studied, and applied to sugar beet to compare different approximation methods including the classical discrete model. With a higher precision, the simulation based on the continuous approach reveal significant differences with the discrete model. Moreover, an approximation of the continuous model is derived with a daily time step, which makes it suitable for agronomy applications.