We report on a global crossover saturated-absorption spectroscopy (SAS) of Cs D2 transition using a dual-frequency laser field with a frequency difference of less than the Doppler width. With two pairs of dual-frequency laser beams counter-propagating through the vapor cell, the line shape and non-linear features observed in the transmission spectra of the probe beam change with the frequency difference of the dual-frequency laser. The superficially complicated transmission signal includes two sets of common single-frequency SAS and several velocity-selective resonances (VSRs), we call these VSR peaks ‘global crossover SAS’. This phenomenon is explained by VSR effect. The global crossover SAS is formed by the atomic velocity groups resonance with both the initial and modulated laser fields, which are counter-propagated. Moreover, the global crossover SAS dips having the separation of allowed hyperfine transitions move along with the two sets of common single-frequency SAS while the frequency difference of the dual-frequency laser is changed. This indicates a resonance between the velocity shifted pump laser frequency and the velocity shifted probe laser frequency. The results obtained in this system are of great interest for laser spectroscopy. Furthermore, the application of the counter-propagating laser beams in the dual-mode regime increase the number of atoms that effectively interact with the field, hence, this scheme has a potential advantage for laser frequency stabilization.