Ab initio methods have been used to explore the unexpectedly strong magnetic anisotropy and the magnetostructural correlations in mononuclear eight-coordinate complex [Co-II(12-crown-4)(2)](2+). Our calculations showed that both decreasing alpha and increasing phi may enhance its magnetic anisotropy, which was rationalized by the qualitative theory proposed by Long and co-workers. Moreover, we deduced that the vertical bar D vertical bar value of [Co-II(12-crown-4)(2)](2+) with alpha = 52 degrees and phi = 43 degrees is the largest one.