By means of ab-initio calculations, we study the surface magnetism of carbon foam, a carbon allotrope constructed by both the sp(2) and sp(3) hybridized carbon atoms. It is found that the sp(3)-terminated surface and sp(2)-terminated surface with hydrogen saturation (sp(2)H) have the antiferromagnetic and ferromagnetic ground states, respectively. And the corresponding phase transition temperatures of these two surfaces are estimated to exceed 100 K. In addition, the magnetic moment of the sp(2)H surface can be effectively modulated by strain. More interestingly, at the level of generalized gradient approximation, as the lattice are stretched, a bulk bandgap will open. And in such a bandgap, the sp(2)H surface states can form spin polarized Dirac cones at K(K ') point. Thus, in the vicinity of the Fermi level, only the electron with a specific spin behaves like a Dirac Fermion. (C) 2014 AIP Publishing LLC.