Abstract: We focus on constructing a novel linear, and fully decoupled scheme for the phase-field dendritic growth model, which not only can have second-order or third-order accuracy in time but also possess energy stability with respect to the original energy. The main techniques we utilize are the implicit-explicit Runge-Kutta (IMEX-RK) method and the stabilization method . In our Runge-Kutta schemes, various coefficient matrices are introduced for different nonlinear terms in the dendritic crystal growth model. Then we propose conditions on coefficient matrices so that the developed scheme satisfies the order conditions while the original energy decay can be proved. Instead of applying existing Runge-Kutta schemes directly, since there are extra conditions on coefficients, we develop an approach to search for coefficient matrices to obtain proper IMEX-RK schemes. We further prove the unconditional energy stability of the scheme strictly and carry out a large number of 2D numerical simulations to verify the accuracy and energy stability.