A steady-state Monte Carlo scheme is developed for phonon transport based on the energy-based deviational phonon Boltzmann transport equation (PBTE). Other than tracking trajectories and time evolution of each packet in the transient methods, this steady-state method determines the paths of energy packets from being emitted to the steady-state through statistics of scattering probability. By reconsidering and developing the periodic heat flux boundary condition, we extend the capability of this method to systems with arbitrary temperature differences. This steady-state energy-based Monte Carlo (SEMC) method has been verified by comparing predictions with results from the previous discrete-ordinates method, the analytical solution, and transient MC methods for phonon transport in or across thin films. The present SEMC algorithm significantly improves the computational efficiency for a steady phonon transport process instead of time evolution by a transient algorithm.