We report production of nanostructured magnetic carbon foam by a high-repetition-rate, high-power laser ablation of glassy carbon in Ar atmosphere. A combination of characterization techniques revealed that the system contains both sp 2 and sp 3 bonded carbon atoms. The material is a form of carbon containing graphitelike sheets with hyperbolic curvature, as proposed for "schwarzite." The foam exhibits ferromagnetic-like behavior up to 90 K, with a narrow hysteresis curve and a high saturation magnetization. Such magnetic properties are very unusual for a carbon allotrope. Detailed analysis excludes impurities as the origin of the magnetic signal. We postulate that localized unpaired spins occur because of topological and bonding defects associated with the sheet curvature, and that these spins are stabilized due to the steric protection offered by the convoluted sheets.