Using the high-resolution near-infrared adaptive optics imaging from the NaCo instrument at the Very Large Telescope, we report the discovery of a new binary companion to the M-dwarf LP 1033-31 and also confirm the binarity of LP 877-72. We have characterized both the stellar systems and estimated the properties of their individual components. We have found that LP 1033-31 AB with the spectral type of M4.5+M4.5 has a projected separation of 6.7 ± 1.3 AU. Whereas with the spectral type of M1+M4, the projected separation of LP 877-72 AB is estimated to be 45.8 ± 0.3 AU. The binary companions of LP 1033-31 AB are found to have similar masses, radii, effective temperatures, and log g with the estimated values of 0.20 ± 0.04 $\rm {M}_{\odot }$ , 0.22 ± 0.03 $\rm {R}_{\odot }$ , and 3200 K, 5.06 ± 0.04. However, the primary of LP 877-72 AB is found to be twice as massive as the secondary with the derived mass of 0.520 ± 0.006 $\rm {M}_{\odot }$ . The radius and log g for the primary of LP 877-72 AB are found to be 1.8 and 0.95 times that of the secondary component with the estimated values of 0.492 ± 0.011 $\rm {R}_{\odot }$ and 4.768 ± 0.005, respectively. With an effective temperature of 3750 ± 15 K, the primary of LP 877-72 AB is also estimated to be ∼400 K hotter than the secondary component. We have also estimated the orbital period of LP 1033-31 and LP 877-72 to be ∼28 and ∼349 yr, respectively. The binding energies for both systems are found to be >10⁴³ erg, which signifies that both systems are stable.