Based on the SU(2) group structure of Jaynes-Cummings model, its time evolution operator were obtained by using the algebraic method. As an application of the solution, the exact result of state |Ψ(t)? of the system evoluting with time at any given time t in the condition that the initial state of system is |e,n? was given. Then, the probability Pe(t) of finding the atom in excited state |e? at time t was obtained in the condition that the initial state of the system is |g,α?. The superiority of the solution was discussed lastly.