This paper examines direct and inverse nonstationary scattering problems for the Dirac-type system on both the whole axis and the semi-axis. It defines the scattering operators for the nonstationary Dirac-type system. Using the Gelfand-Levitan-Marchenko type equations, we prove the unique reconstruction of the potential from the scattering operator on the whole axis. Additionally, we establish the uniqueness of the inverse scattering problem for the Dirac-type system on the semi-axis by the relationship between the scattering operators on the whole and semi-axis.