Housing is one of the basic needs of an individual and the quality of life of the individual and thus a basic component in determining the quality of life of an individual. Successive administrations in Nigeria have made efforts to increase the quantity of available housing stock without much success. The implementation of green building principles is an imperative in the provision of housing for the low/medium income households in Nigeria. Generally, green building developments are believed to be more costly than the conventional building developments, there is a lack of willingness to embrace green building principles. However a critical review of literature show a minimal increase in the initial cost of sustainable building projects with significant savings in future costs of such projects. The study also observed that high cost has been one of the challenges to the provision of affordable housing in Nigeria. Since the decision to build or not is greatly influenced by the perceived initial capital outlay, the lack of an appropriate tool to have a predictive knowledge of the cost of the intended project has been a clog in the wheel of green building development generally, Nigeria inclusive. Review of literature reveals that there are cost prediction tools that can be effectively used to assess sustainable building development. The chapter concludes that the use of predictive models will help to moderate the cost of intended green building projects thereby keeping within the affordable range of the intended owners. It is recommended that if these tools are adequately employed, it will influence the adoption of green building principles for the provision of affordable housing in Nigeria. The Artificial Neural Network is recommended for the development of cost models giving the minimal rate of percentage error associated with its use.