Noether theorems for Lagrangian and Hamiltonian systems in terms of combined Caputo derivative on time scales are investigated. Firstly, the definition of the combined Caputo derivative on time scales is given; Secondly, differential equations of motion in terms of the combined Caputo derivative on time scales are presented; Thirdly, Noether identities and conserved quantities for those two systems are studied separately; Fourthly, examples are provided.