We propose a class of Runge-Kutta methods which provide a simple unified framework to solve the gradient flow of a convex functional in an unconditionally energy stable manner. Stiffly accurate Runge-Kutta methods are high order accurate in terms of time and also assure the energy stability for any time step size when they satisfy the positive definite condition. We provide a detailed proof of the unconditional energy stability as well as unique solvability of the proposed scheme. We demonstrate the accuracy and stability of the proposed methods using numerical experiments for a specific example. (C) 2019 Elsevier B.V. All rights reserved.