In this paper, we study on the cutting plane methods for Lagrangian relaxation based unit commitment algorithm. In the algorithm, non-differentiable optimization methods can be applied to optimize the dual function, and a subgradient method which needs parameter tuning and has some drawbacks such as computational inefficiency and oscillating behavior is commonly used. The cutting plane method and the central cutting plane method are applied to the algorithm and implemented using re-optimization techniques. Numerical example shows that both methods are accelerated by the re-optimization techniques and have good convergence property without parameter tuning.