This paper aims to study the design of a climbing robot with an embedded permanent magnetic matrix (EPMM) wheel. There are a number of advantages for an EPMM wheel including lighter weight, lower cost and higher degree of adaptability compared to a donut permanent magnet wheel. The magnetic adhesive force on the EPMM wheel can be adjusted by changing the wheel configurations such as number of magnets embedded in the wheel, the thickness of flange and the flange geometry. From various experiments, the EPMM wheel design guidelines are proposed for ferromagnetic wall climbing robot applications.