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We calculate the coupling constants of the decay modes 1−+ → ρπ, f1π, b1π, ηπ, ήπ, a1π, f1η within the framework of the light-cone QCD sum rule. Then we calculate the partial widths of these decay channels, which differ greatly from the existing calculations using phenomenological models. For the isovector 1−+ state, the dominant decay modes are ρπ, f1π. For its isoscalar partner, its dominant decay mode is a1π. We also discuss the possible search of the 1−+ state at BESIII, for example through the decay chains J/ψ(ψ’) → π1 + γ or J/ψ(ψ’) → π1 + ρ where π1 can be reconstructed through the decay modes π1 → ρπ → π+π-π0 or π1 → f1(1285)π0. Hopefully the present work will be helpful to the experimental establishment of the 1−+ hybrid meson.