In this study, we intend to determine the coupling properties of the fundamental mode HE₁₁ with respect to the high-order core vector modes (TE₀₁, TM₀₁, and HE₂₁) in case of the mechanically induced microbend long-period fiber gratings (MLPGs). Therefore, the effects of various parameters, including the grating period, microbend amplitude, and coupling coefficient, on the coupling of the vector modes in the MLPGs were analyzed with respect to the step-index and inverse-parabolic-index fibers. The results denote that the coupling coefficient plays a critical role during the mode coupling process and that the strength of vector mode coupling can be effectively tuned by applying pressure to vary the microbend amplitude of the fibers. The MLPGs of the inverse-parabolic-index fiber can convert the high-order vector modes (TE₀₁, TM₀₁, and HE₂₁) at specific wavelengths, and the resonant wavelength obtained using the high-order mode can be tuned. The MLPGs possess potential application value with respect to vector mode multiplexing, orbital angular momentum generation, and multiplexing.