A new hexaprismane Co(II)(6)(mu(3)-OH)(6) cluster-based three-dimensional coordination polymer (\{Co(mu(3)-OH)-(HCOO)(0.72)(CH3COO)(0.28)\}(n), Co6-CP) was successfully synthesized and characterized with single-crystal XRD, IR spectra, TGA spectra and elemental analysis. Co6-CP was used as an effective heterogeneous catalyst for the aerobic epoxidation of various alkenes. For the catalytic epoxidation of trans-stilbene, the conversion and selectivity towards the epoxide reached 98.6 and 98.0\%, respectively. Also, an average TOF of 22 h(-1) was obtained for the reaction. The results indicated that Co6-CP displayed excellent aerobic epoxidation activity among the reported coordination polymer materials, even rivaling the traditional heterogeneous cobalt catalysts. The influence of the reaction parameters such as temperature and oxygen flow rate for the epoxidation of the trans-stilbene were also studied in detail.