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 characterised 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 \pm 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 \pm 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 \pm 0.04 M _ { \odot } , 0.22 \pm 0.03 R _ { \odot } , 3200 K , 5.06 \pm 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 \pm 0.006 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 \pm 0.011 R _ { \odot } and 4.768 \pm 0.005 , respectively . With an effective temperature of 3750 \pm 15 K , the primary of LP 877-72 AB is also estimated to be \sim 400 K hotter than the secondary component . We have also estimated the orbital period of LP 1033-31 and LP 877-72 to be \sim 28 and \sim 349 yr , respectively . The binding energies for both systems are found to be > 10 ^ { 43 } erg , which signifies both systems are stable .