This study is devoted to investigate the phase diagrams of 3-state Potts model with competing binary, ternary and quaternary interactions on Cayley tree. The 3-state Potts model was classified as the simplest quantum field-theory after Ising model and was an easily defined class of statistical mechanic model. The aim of this study is to analyze the phase diagrams of 3-state Potts model with competing interactions on Cayley tree of order 2 and 3. At vanishing temperature T, the phase diagrams are fully determined for all values of competing binary interactions J 1 , ternary interactions J t and quaternary interactions J q. The results show that there have significant change~ in the phase diagrams for the case of nonzero ]q. Lastly, we analyze in detail the set of modulated phases, with the phase being indicated by many different types of commensurate and incommensurate phases by plotting the wavevectors versus temperature. The Lyapunov exponent is computed to verify the stability of the large period phase in the narrow-interval modulated phase.