Stimulated Brillouin scattering (SBS) in a few-mode fiber (FMF) is of significance for the distributed temperature and strain sensing. An FMF with M-shaped refractive index distribution (M-FMF) is proposed in order to improve the performance of simultaneous temperature and strain sensing based on SBS. Propagation of four optical modes is supported by the M-FMF, so that the Brillouin gain spectrum (BGS) can be obtained by both intra-mode and inter-mode SBS. The BGSs produced by the interactions of LP₀₁-LP₀₁ mode pair, LP₀₁-LP₁₁ mode pair, and LP₁₁-LP₁₁ mode pair are analyzed, respectively. Meanwhile, the temperature and strain sensing performance based on the BGS of LP₀₁-LP₁₁ mode pair are studied in detail. Considering a common step-index FMF, only one obvious scattering peak is usually present in the BGS obtained from the interaction between different optical mode pairs, therefore, it is inconvenient to achieve multi-parameter sensing measurement. In this paper, the BGS of LP₀₁-LP₁₁ mode pair has two scattering peaks, which are contributed by the acousto-optic coupling between the acoustic modes L_1n (n = 1, 2) and the optical modes LP₀₁ and LP₁₁. The two Brillouin scattering peaks have large gain values of 0.1004 m^–1·W^–1 and 0.0463 m^–1·W^–1, respectively. More importantly, the gain difference between two Brillouin scattering peaks is small, and the frequency interval is 75 MHz, which can be applied to simultaneous temperature and strain sensing. The influences of the refractive index and the fiber core radius on the BGS of LP₀₁-LP₁₁ mode pair are studied. By selecting the optimal structure parameters, we discuss the effect of temperature and strain on the BGS of LP₀₁-LP₁₁ mode pair. The errors for simultaneous temperature and strain measurement are reduced to 0.23 ℃ and 5.67 με. Compared with other reported results, our obtained temperature and strain sensitivity are high and sensing errors are low in the considered M-FMF. In other words, based on the BGS of LP₀₁-LP₁₁ mode pair, the performance of temperature and strain sensing are improved in the M-FMF. This work is of great significance for studying intra-mode and inter-mode SBS in an FMF. Moreover, the results also provide a guideline for further improving the performance of simultaneous temperature and strain sensing.