To understand the evolution of cognitive abilities, we need to understand both how selection acts upon them and their genetic (co)variance structure. Recent work suggests that there are fitness consequences for free-living individuals with particular cognitive abilities. However, our current understanding of the heritability of these abilities is restricted to domesticated species subjected to artificial selection. We investigated genetic variance for, and genetic correlations among four cognitive abilities: inhibitory control, visual and spatial discrimination, and spatial ability, measured on >450 pheasants, Phasianus colchicus, over 4 generations. Pheasants were reared in captivity but bred from adults that lived in the wild and hence, were subject to selection on survival. Pheasant chicks are precocial and were reared without parents, enabling us to standardise environmental and parental care effects. We constructed a pedigree based on 15 microsatellite loci and implemented animal models to estimate heritability. We found moderate heritabilities for discrimination learning and inhibitory control (h²=0.17-0.23) but heritability for spatial ability was low (h²=0.09). Genetic correlations among-traits were largely positive but characterised by high uncertainty and were not statistically significant. Principle component analysis of the genetic correlation matrix estimate revealed a leading component that explained 69% of the variation, broadly in line with expectations under a general intelligence model of cognition. However, this pattern was not apparent in the phenotypic correlation structure which was more consistent with a modular view of animal cognition. Our findings highlight that the expression of cognitive traits is influenced by environmental factors which masks the underlying genetic structure.