A two-pulse bidirectional propagating amplification configuration, which employs two laser pulses to propagate along a main amplifier in two directions of symmetric space and amplifies the two-pulse, can effectively increase the extraction efficiency for the stored energy in the amplifier, and has great application value in the field of inertial confinement fusion laser driver. When we build the equivalent optical path, the wave-front distortion superposition process of the two laser pulses in the process of propagation amplification is derived, and the numerical simulation is carried out with the data measured by the Shenguang-Ⅲ host device. The results indicate that the wave-front shapes of the two laser pulses in the bidirectional propagating amplification configuration are different. The wave-front aberration mainly concentrates in low frequency range. Moreover, the wave-front distortions of the output laser pulse and the laser pulse from the pinhole of spatial filter which is with three-pass and four-pass amplification are large. Thus, the wave-front aberration must be compensated and controlled to ensure the quality of output beam and the beam pass through the spatial filter pinhole. These conclusions will provide theoretical guidance for the design of wave-front control scheme of two-pulse bidirectional propagating amplification configuration.