The present invention concerns a high power density solid oxide fuel cell having a cathode, electrolyte and graded porous anode. The graded porosity of the anode allows easy transport of fuel gases thereby minimizing concentration polarization. Power densities of about 1.8 W/cm2 at 800° C. and about 0.8 W/cm2 at about 650° C. have been achieved with graded porous anodes as thick as 0.75 mm. These fuel cells having a graded porous anode are more durable and mechanically reliable than those found in the art.