The convection heat transfer for natural flow of air over an isothermal vertical surface embedded with porous metal foam was theoretically studied using boundary-layer theory and local thermal equilibrium assumption. The conservation equations were simplified by analyzing the order of magnitude of each term and then solved by using integration method. It was shown that the develop of fluid boundary-layer thickness with metal foam was much faster than that of plain vertical surface because of disturbances induced by metal foam. The fluid boundary-layer thickness grew faster with larger porosity and higher pore density(porosity 0.9—0.95 and pore density 5—40 PPI).The flow velocity of air reached the maximum quickly and kept almost constant. The heat transfer in porous aluminum with 0.9 porosity and pore density 5 PPI was enhanced more than 9 times compared with that of plain vertical surface. However，with further increase in porosity and pore density，the develop of fluid boundary-layer thickness was too fast，which made heat transfer worse.