The symplectic structure, which has its roots in the study of Hamiltonian systems [1], provides a framework in the field of symplectic geometry. This framework is important for preserving the geometric properties of a system during numerical integration for maintaining the accuracy and stability of solutions over time, especially in longerm simulations. The objective of this study is to design symplectic algorithms developed for numerically solving optimal control problems, which arise in engineering problems such as trajectory planning, wing profile design, or general parameter fitting. In the context of optimal control problems, optimal solutions satisfy a system of differential algebraic equations that are derived from Pontryagin’s Maximum Principle. This principle states the necessary conditions that enable us to formulate Hamiltonian boundary-value problems that might be tackled using symplectic methods. We will introduce algorithms that preserves the symplectic structure for the numerical discretisation of optimal control, and illustrate its properties in linear and non-linear problems.