In economic growth theory, product and process innovations are critical factors contributing to technological progress. This study constructs an economic growth model that considers product and process innovations and theoretically investigates how these two types of innovation affect economic growth and unemployment rates. Using our model, based on Zagler (Int Rev Appl Econ 18:209–224, 2004), we obtain the following three main findings: (1) an increase in the efficiency of product innovation increases both the economic growth and unemployment rates; (2) an increase in the efficiency of process innovation increases the economic growth rate but does not affect the unemployment rate; and (3) a decrease in labor allocation to product innovation and an increase in labor allocation to process innovation in the R & D sector increase the economic growth rate and decrease the unemployment rate depending on the conditions. These findings suggest that to simultaneously raise employment and increase economic growth, we need not only a policy for fostering product innovation but also another policy to improve employment.