Family businesses represent a very important part of every economy, because they create the foundations for economic stability. The concept of strategic management is linked to the business operations of companies in general, including family businesses, which refers to one of the main links of a company that offers the possibility of looking at long-term business and the realization of a sustainable competitive advantage. A case study of the family company Sokol d.o.o. from Vinkovci was selected for this research. It has been successfully engaged in construction for many years and operates stably and in accordance with socially responsible business and environmental protection, so that they have received as many as 10 certificates of excellence for their activities. The company is in a positive environment, where it has resources that enable it to grow, but competition, innovation and market opportunities are a constant challenge in the construction industry. The main goal of this research was to analyze the possibilities and propose the most suitable growth strategy. For the analysis of the external and internal environment, the usual strategic tools were used (PEST, SWOT, sector and competition analysis, analysis of financial reports, etc.) and Allan Gibb's Growth Framework suitable for the analysis of the growth of small and medium-sized family enterprises. At the end, a market development strategy was proposed through the expansion of the company with its services to new markets, especially foreign markets. For the realization of this strategy, firstly it will be necessary to update the website of the company Sokol d.o.o. and create accounts on social networks. In order to attract and retain the best quality workers, it is necessary to create even more favorable working conditions and systematically work on the image of a desirable employer. For further research on the growth strategies of family businesses, it is recommended to definitely include issues of generational transition and the opinions of potential heirs on sustainable growth.