There is need for Kenyan small and medium enterprises (SMEs) in particular to focus concern on the orientation of business strategy toward global market strategy, market research geared at obtaining foreign market intelligence, innovation and technology, product adaptation, service orientation, collaborative ventures, and longrange vision as critical factors in making them successful in the international market. They also need to interact effectively with other firms in more or less tightly connected networks of shared production and innovation if they are to succeed in the current wave of globalization. The purpose of this study was to investigate the role of global market strategy on the global expansion of Kenyan firms. The research study used descriptive and inferential design as a chosen design. The researcher used multiple/multivariate regression analysis to determine the functional relationship between the independent variables and the dependent variable. The global market strategy variables considered include the following: market strategy incorporating: global advertising and promotion, external advisory services, foreign market specialization, competitive pricing strategies, and focus on quality products/ services; foreign market intelligence on locating markets, trade restrictions, competition overseas, and market and investment opportunities; and logistics and distribution incorporating: handling of documentation, distribution coordination, warehousing, arranging transportation, and collaboration with large firms. A random sample of 205 firms was drawn out of 440 members of Kenya Association of Manufacturers, based in Nairobi, from the Kenya Association of Manufacturers and Exporters Directory of 2012. The senior management of selected firms was surveyed and 175 firms responded making a response rate of 85 percent. The key finding from the research is that there is a functional relationship between global market strategy and global expansion of SMEs. The implication for practice and policy is that there is a need for collaboration between industry and government in pursuing policies for global expansion and among SMEs and large enterprises particularly in developing capacity and collaboration in global marketing strategy, market intelligence gathering, export promotion and strengthening of foreign trade missions. An earlywarning system to alert firms of changes that may lead to potential failure in their global business activities can be developed.