We present a unique design of weakly coupled few-mode photonic crystal fiber (FM-PCF), which can support six vector modes (HE_11a,HE_11b,TM₀₁,HE_21a,HE_21b, and TE₀₁) with ultra-flattened chromatic dispersion over the C wavelength band. We investigate the impact of fiber parameters on chromatic dispersion, minimum effective refractive index difference (minΔn_eff), confinement loss, bending loss, and differential mode delay using the finite element method. To achieve ultra-flattened chromatic dispersion and large minΔn_eff, an extra small elliptical defected hole is introduced in the fiber core. The circular holes in the first ring are replaced by elliptical holes to further obtain flattened-chromatic dispersion. The simulated results show that the designed weakly coupled FM-PCF can obtain an ultra-flattened average dispersion of 0.011 ns/nm/km with a small dispersion slope (<1.5  ×  10^−  5  ns  /  km  /  nm²) in the wavelength range of 1520 to 1570 nm. And the proposed weakly coupled FM-PCF has large minΔn_eff (>1  ×  ^{10  −  3}), low confinement loss (<10^−  4  dB  /  km), and good bending resistance. In summary, the proposed weakly coupled FM-PCF has potential applications for large-capacity MDM communication systems.