Information technology has an increasingly strong demand for high-speed and large-capacity optical fiber networks. Space division multiplex(SDM) is a new generation of optical fiber communication technology which can be several times in communication capacity higher than the wavelength division multiplexing systems. In this paper, we present a kind of 13-core 5-mode fiber with double trench structure to meet the demand for high-speed and large-capacity information transmission in the future. In order to solve the crosstalk problem in SDM, a double-trench structure is adopted to better limit the light energy in the fiber core, thus reducing the crosstalk between cores and modes. The crosstalk and transmission characteristics of multi-core fiber are calculated and analyzed by the full vector finite element method and coupled power theory. After the optimization of structural parameters, the fiber can stably transmit LP ₀₁, LP ₁₁, LP ₂₁, LP ₀₂and LP ₃₁in the band of 1.3–1.7 μm; when the signal is transmitted at the 1.55 μm for 60 km, the inter-core crosstalks corresponding to the adjacent fiber cores in the above five modes are –122.37 dB, –114.76 dB, –106.28 dB, –100.68 dB and –92.813 dB, respectively; the effective refractive index difference between adjacent modes is greater than 1.026 × 10 ^–3; inter-core and inter-mode crosstalk can be effectively suppressed. The corresponding non-linear coefficients of the 5-modes are 0.74 W ^–1·km ^–1, 0.82 W ^–1·km ^–1, 0.88 W ^–1·km ^–1, 1.26 W ^–1·km ^–1, 0.93 W ^–1·km ^–1, which can maintain low non-linear transmission. The structure of fiber is simple and compact, and the preform can be fabricated by vapor deposition method and stack method, then the 13-core five-mode fiber with low crosstalk and low nonlinear can be further drawn, which can be used in a long distance high-speed and large-capacity fiber transmission system.