This study analyses the initial returns of initial public offerings (IPOs) using a sample of companies listed in the Nairobi Stock Exchange during the period 1984 to 2008. It further relates the initial return to subscription rate using regression models to establish whether relationship exists and the nature of the relationship. The study provides one emerging market case of international evidence on performance of IPOs. The findings from the sampled IPO firms show an average initial return of 40.28% on the first day of trading in the secondary market. This represents 17.78% increase when compared with study by Maina (2004) when he found initial return of 22.57%. All this is consistent with other international research, which have on average also documented first day positive initial returns. See appendix 5. The study also found out that Quadratic regression model best represents the nature of relationship between initial return and subscription rate when compared with results generated by linear regression model in the Kenyan IPO market.