A new Co(II)-based coordination polymer, [{Co₃(ina)_7.5(μ₃–O)}{Co₃(ina)_2.5(μ₃–OH)(μ–OH)(C₂H₅OH)(H₂O)₂}₃]NO₃·3C₂H₅OH·24H₂O (1, also denoted as MCF-39), has been synthesized from the solvothermal reaction of cobalt(II) nitrate and the ligand isonicotinic acid (Hina) with the presence of hmq (2-(hydroxymethyl)-quinolin-8-ol) as a necessary additive. The crystal structure of 1 consists of the 7- and 9-connected trinuclear clusters, and exhibits the first highly-connected binodal network with (3⁴·4⁹·5⁶·6²)₃(3⁶·4¹⁵·5¹⁵) topology. Magnetic studies show that the spin canting and spin-glass-like behaviours were found in 1, and the cooperative effect among intra- and inter-trimer could greatly influence the bulk magnetic behaviour of the three-dimensional (3D) framework.