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