Highly intense backward first-Stokes (BS1) in CH4 is generated by using a single longitudinal mode second-harmonic Nd∶YAG laser [532 nm, linewidth Δνp <100 MHz， pulse-width (FWHM) 6.5 ns] as the pump source, which is radically different from previous reports where the output from a longer pulse-width (30 ns) pump laser is mainly stimulated Brillouin scattering (SBS). This is because that in authors' experiments the pulse-width is comparable with the SBS phonon lifetime that results in a transient SBS process. According to authors' calculation, the gain coefficient for the transient SBS in the present case is already somewhat lower than that of BS1, and SBS is suppressed by BS1. Under a CH4 pressure of 1.1 MPa, a pump laser repetition rate 2 Hz and laser pulse energy 95 mJ, the quantum conversion efficiency of BS1 is as high as 73%. Due to the relaxation oscillation, the BS1 pulses are narrowed to about 1.2 ns. As a result, the BS1 peak power turns out to be 2.7 times that of the pump. Furthermore, the beam quality of BS1 is much better than that of the pump. The relaxation oscillation in the experimental BS1 temporal waveform is well reproduced by a calculation using a quasi-two dimensional computer program.