Attosecond transient absorption (ATA) spectroscopy is a very useful technique for studying the ultrafast dynamics of electrons in atoms or molecules on sub-femtosecond timescale. The time-dependent Schr?dinger equation is numerically solved to simulate the evolution of hydrogen molecular ion ( H2+) in the intense near infrared (NIR) and extreme ultraviolet (XUV) composite laser field and to examine the ATA spectroscopy under the nuclei-fixed or nuclei-movable condition. The research shows that when the nuclei is fixed, the resulting ATA spectroscopy is similar to those of atoms. In contrast, when the nuclei is not fixed, the ATA spectroscopy exhibits richer periodically-modulated absorption line structures, whose modulation period is just equal to half of the NIR laser period. By analyzing the ionization-dissociation characteristics of H2+, we clarify the origin of such half-periodic modulation as quantum interference among different quantum transition paths from ground to excited states. Comparing the ATA spectroscopy under different situations, one can easily distinguish the obvious influence of nuclear motion on molecular ATA spectroscopy.