A foam wall panel system with a unique Z-shaped wall stud. The Z-shape of the wall stud provides cavities on each side which accept the angled edges of foam wall panels that fit within the cavities. Adjacent foam wall panels having angled edges are secured into the cavities on opposite sides of Z-shaped wall stud to form a continuous foam wall. The Z-shaped wall stud can be fabricated from a single sheet of metal, or other suitable materials capable of replacing metal wall studs. The folded corner edges of the Z-shaped wall stud, and the edges of the foam panels, are rounded to avoid damage to the foam wall panel during the installation process. An alternative embodiment provides angled gripping edges on the Z-shaped wall stud that secures the foam panels to the Z-shaped wall stud.