In this paper, by virtue of a finite element method, we studied the mode field characteristics, evanescent field characteristics, and bending loss of a weakly-coupled eccentric-core few-mode fiber in higher-order modes. Furthermore, we investigated the influence of fiber parameters on the minimum effective refractive index difference between adjacent modes, and optimized the fiber to support 10 linearly polarized modes and satisfy the weak coupling condition. In addition, we analyzed the power distribution and bending loss of the 10 modes at the wavelength of 1550 nm. The research results indicate that the minimum effective refractive index difference between adjacent modes is larger than 10 ^-4 over the whole C-band. Besides, the fiber shows higher evanescent field intensity, higher sensing sensitivity and larger bending loss in higher-order modes and can distinguish a specific bending direction. In conclusion, these results have potential application value for improving the sensitivity of sensors.