The solvothermal reaction of DyCl3 center dot 6H(2)O, Ni(NO3)(2)center dot 6H(2)O, and H(4)abtc ligands (H(4)abtc = 3,3',5,5'-azobenzene-tetracarboxylic acid) in the mixed DMF/H2O solvents (DMF = N,N-dimethylformamide) produced a three-dimensional (3D) Ni-II-Dy-III heterometallic coordination polymer (HCP) formulated as {[NH2(CH3)(2)](2)[NiDy2(HCOO)(2)(abtc)(2)]}(n) (1). In 1, Dy-III and Ni-II ions interconnect through carboxylic O donors of abtc(4-) ligands to generate a linear trimer "Hourglass"-type {NiDy2} cluster, and the adjacent trinuclear {NiDy2} units are bridged by HCOO- groups to give a 1D "ladder" chain, which is further bridged by abtc(4-) ligands to form a new topology and named as "zsw3". Alternating-current magnetic susceptibility results indicate that 1 exhibits frequency-dependent out-of-phase signals with two relaxation processes, which suggests that it shows single-molecule magnet (SMM) behavior and represents the first example by using an SMM cluster as the building block to create a 3D Ni-Ln HCP, to the best of our knowledge. The energy barriers for 1 under a 1000 Oe applied direct current magnetic field are estimated from Arrhenius plots to be 40 and 42 K at higher and lower frequencies, respectively. Additionally, the crystalline structure of 1 could be stable to at least 310 degrees C, supported by thermogravimetric analyses and in situ variable-temperature powder X-ray diffraction patterns.