PROBLEM TO BE SOLVED: To provide a method for serum-free culture of mesenchymal stem cells and a serum-free medium for the culture.SOLUTION: There is provided a method for primary culture of mesenchymal stem cells to culture the mesenchymal stem cells originated from human adipose tissue by using a serum-free medium. Preferably, the medium is added with reduced glutathione and fibronectin. The medium may be further added with ecotin and ultra-low molecular weight hyaluronic acid. There are further provided a mesenchymal stem cell population prepared by culturing by the culture method and an Alzheimer's disease treatment agent containing the mesenchymal stem cell population obtained by the method as an active component.