The dynamics of entanglement of three two-level atoms initially in GHZ state system interacting with a Fock state field are investigated by means of concurrence and linear entropy. The effect of photon number on the time evolution of concurrence and linear entropy is analyzed. The results show that the phenomenon of sudden birth of entanglement between two atoms trapped in a cavity occurs and the threshold time and maximum for the creation of the entanglement can be controlled by the photon number. The measurement of the atom outside the cavity leads to the periodic evolution of the concurrence and an increase of the photon number results in decreasing in the maximum of concurrence and shortening of the evolution period of the time behavior of concurrence.