Stimulated Raman scattering (SRS) is a powerful tool for the extension of the spectral range of lasers. To obtain efficient Raman conversion in SRS, many researchers have studied different types of Raman laser configurations. Among these configurations, the intra-cavity type is particularly attractive. Intra-cavity SRS has the advantages of high intra-cavity laser intensity, low-SRS threshold, and high Raman conversion efficiency. In this paper, An Q-switched intra-cavity Nd: YAG/CH4 frequency-doubled Raman lasers is reported. A negative branch confocal resonator with M= 1.25 is used for the frequency-doubling of Nd: YAG laser. The consequent 532nm light is confined in intra- cavity SRS with travelling wave resonator, and the focal of one mirror of cavity is overlap with the center of the other mirror of the cavity. We found this design is especially efficient to reduce the threshold of SRS, and increase conversion efficiency. The threshold is measured to be 0.62 MW, and at the pump energy of 16.1 mJ, the conversion efficiency is 34%. With the smaller magnification M, the threshold could further decrease, and the conversion efficiency could be improved further. This is a successful try to extend the spectral range of a laser to the shorter wavelength by SRS, and this design may play an important role in the fulfillment of high power red lasers.