On the basis of the two-component coupled Hirota equation, the higher-order solitons solution of the equation is investigated, and dynamical characteristics is analyzed. Based on the Lax pair and generalized Darboux transformation, the Taylor expansion of the characteristic function is carried out, and the expressions of the second-order and third-order soliton solutions of Hirota equation are derived. The real and imaginary parts of spectral parameter λ are discussed in different cases. Under the influence of the value of different free parameters, the evolution graphs of soliton interaction are obtained via numerical simulation. The effects of different parameters on the amplitude change and propagation direction of solitons are analyzed. The results show that different values of parameters affect the interaction and propagation direction of solitons.