A series of ZnII-DyIII complexes with molecular formula [LZn(CH3COO)Dy(hfac)2] (1), [LZn(CH3COO)2Dy(dbm)]·CH2Cl2 (2), [LZn(CH3COO)Dy(btfa)2]·CH2Cl2 (3), (H2L = N,N'-bis(3-methoxysalicylidene)-1,2-phenylenediamine, hfac = hexafluoroacetylacetone, dbm = dibenzoylmethane, btfa = benzoyltrifluoride acetone) were structurally and magnetically characterized. They have similar ZnII-DyIII structural cores bridged by N and O atoms of the hexadentate salen type ligand (L). The main difference between them is the peripheral β-diketonate co-ligands surrounding DyIII ion. Dynamic magnetic properties measurements revealed that complexes 1-3 exhibit the field-induced SMM behavior with relaxation energy barriers Ueff/kB of 45.49 K, 69.28 K and 101.34 K, respectively. The ac magnetic susceptibility of diluted sample 3Dy0.05Y0.95 confirmed the single molecule original relaxation, in which the quantum tunneling of magnetization (QTM) was suppressed efficiently and a butterfly-shaped hysteresis loop at 1.8 K was observed.