We propose a heterogeneous thirteen-core few-mode fiber, which has the excellent characteristics of low crosstalk (XT), large effective mode field area (Aeff) and low dispersion slope (Dslope). The double high refractive index ring can precisely control the effective refractive index difference between the LP mode in the core and reduce intra-core XT. The relative spatial efficiency (RSE) of the 13-core 6-mode fiber reaches 33.84, and the number of spatial channels is as high as 130. The inter-core crosstalk is less than −60 dB/km at 1550 nm. The results show that the proposed fiber with low crosstalk and large Aeff is sufficient to satisfy the requirements of long-distance transmission in the future.