The capacity of a traditional optical communication system based on single-mode fiber has approached to its theoretical limit. Multi-core few-mode fibers provide an effective way to break through the bottleneck of existing transmission capacity. In this paper, a 5-LP-mode weakly-coupled low-crosstalk 7-core fiber is designed by using a combination of trench assistance and air hole isolation structure. The fiber with a standard outer diameter achieves low crosstalk between cores and modes. The inter-core crosstalk area and the effective mode area of the core are calculated by the finite element method. After design optimization, there are 5 stable transmission LP modes in the C+L band of optical communication in this fiber. The effective refractive index difference between LP₂₁ mode and LP₀₂ mode is the smallest and is greater than 1.1 × 10^–3. The LP₃₁ mode in the optical fiber has the largest inter-core crosstalk and the loss is lower than –50 dB/km. The fiber can achieve low crosstalk transmission between modes and cores at the same time. The mode areas of the 5 LP modes in the 7 cores are larger than 86 μm², and the relative core multiplexing factor is 57.63 at a wavelength of 1550 nm. Therefore, this fiber can be used in a large-capacity high-speed fiber transmission system.