The present study investigates the structure of of-complement noun phrase in Nigerian English, comparing findings with those of British and Ghanaian varieties. Of-complement is high in frequency and is a typical complement that has structural tendencies for recursiveness and complexity. A review of literature explicating the structural simplification hypothesis (Gorlach, 1998) suggests that the structure of-complement (or any other type) has received very little attention. Perhaps such scanty works show the different arguments surrounding its syntactic and theoretical status in different grammatical descriptions. Unlike many previous NP frameworks, Huddleston & Pullum (2002, 2004) argued that complements are not only a syntactic element within the NP structure, but also that they are of equal obligatory syntactic status as a head noun within an NP. This framework, unlike many others, therefore conceptualizes the complement slot as an important part in the scheme of things for an NP structure viz-a-viz its complexity. Thus, a serious examination of NP complexity would consider the cooperation (relationship) between a complement and the other syntactic elements constituting the NP structure. This is one of many issues that the present study sheds light on. On the basis of variables representing syntactic function and text type, together with corpus analyses of NPs extracted from the Nigerian component of International Corpus of English (ICE), the structural behavior of of-complement in the lights of other internal elements constituting an NP structure, is clearly shown. It is found that a complement is less likely to co-occur with other all internal elements (20%). Also, it is shown that an of-complement is likely to co-occur with prenominal elements (30%). Furthermore, the paper shows that a structural type of of-complement representing h-complement (i.e. an NP structure consisting of a head noun + a complement, see Huddleston & Pullum, 2002, 2004, and Akinlotan & Housen, 2017) is more likely to occur (26%) as an independent NP structure than to co-occur with postnominal elements (24%). The structural simplification hypothesis is manifested in our corpus data, as it is found out that a complement is more likely to be simple-structured (54%) than complex-structured (46%). On the predictive strength of syntactic function and text type (Biber et al., 1999; Schilk & Schuab, 2016; Akinlotan, 2017), the study finds syntactic function a better predictor than text type.