Study on dual-mode large-mode-area multi-core fiber with air-hole

•The fiber can realize strict dual-mode operation (HE11 mode and HE21 mode) and reduce mode coupling.•Effective area of fundamental mode is up to 1423.972 μm2 by optimizing structural parameters, which can reduce nonlinear effect in the fiber and increase transmission capacity.•Bending loss of the fiber is less than 10-4dB/m at R > 0.26 m, which can be used for FTTH.•The fiber has potential in large number of high power optical fiber devices.