The private sector is said to be the engine of economic growth for a country, especially, for developing economies. Ghana, discovering crude oil in commercial quantities in 2007 coupled with its new lower-middle income status in 2010, has become the focus for many investors. Meanwhile, the private sector of Ghana has suffered crowding out due to stiff competition from the public sector for the meager funds available in the domestic banks for their activities. This study aims at investigating the factors that influence domestic credit to the private sector in Ghana. The study used panel data spanning the period from 1961 to 2016. The results from the use of Johansen cointegration and vector auto-regression show that, though there is no long-run association among the variables, there exist significant short-run relationship between domestic credit to the private sector, broad money and gross capital formation. Further diagnostic tests showed that gross capital formation Grangercauses both domestic credit to the private sector and broad money, and domestic credit to the private sector Granger-causes broad money. The study concluded that money supply and gross capital formation are necessary factors to address in the quest for developing the financial strength of domestic banks in providing credit facilities to the private sector for economic growth. The findings will help policy makers in Ghana to take informed decisions when tackling economic growth issues.