We study the up-down asymmetries in the three-body anti-triplet charmed baryon decays ofwhile B n and M ( ′ ) denote octet baryon and meson states, respectively. By assuming the s-wave meson-pairs to be the dominant constituents in final state configurations, we can write the spin-dependent decay amplitude into parity-conserving and parity-violating parts, parametrized by 6 real parameters under SU (3) f , respectively. Fitting these parameters by 16 experimental data points with the minimum χ 2 method, we obtain that χ 2 /d.o.f = 2.4, which a reasonable fit. With the fitted parameters, we evaluate the up-down asymmetries along with the decay branching ratios of B c → B n M M ′ . Some of these up-down asymmetries are accessible to the experiments at BESIII, BELLE-II and LHCb.