The capacity of the traditional optical communication system based on single-mode fiber has approached 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 standard outer diameter achieves low crosstalk between cores and modes. Inter-core crosstalk and 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. Among them, the effective refractive index difference between LP21 and LP02 modes 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 -50dB/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 86μm2, and the Relative Core Multiplexing Factor is 57.63 at the wavelength of 1550nm. Therefore, this fiber can be used in large-capacity high-speed fiber transmission system.