This paper reports the experimental study of the single-pass and cascaded stimulated Raman scattering (SRS) of deuterium gas in anti-resonance hollow-core fibers (AR-HCFs). The process of SRS of deuterium gas in AR-HCF is analyzed in detail and the variations in the output spectrum and Raman power with the pressure of deuterium gas and the pump laser power are studied as well. It is found that the rotational SRS can be effectively suppressed and the efficiency of vibrational SRS is improved by reducing the pressure and using pump laser pulses with a relatively low peak power. In addition, by further designing and fabricating an AR-HCF with transmission bands in the right position and narrow bandwidths, efficient first-order vibrational Stokes light (1561 nm) and second-order cascaded vibrational Stokes light (2925 nm) can be output via pumping with a 1064 nm pulsed laser.