We show that there is a fermionic minimal model, i.e., a 1+1D conformal field theory which contains operators of half-integral spins in its spectrum, for each c=1-6/m(m+1), m≥3. This generalizes the Majorana fermion for c=1/2, m=3 and the smallest N=1 supersymmetric minimal model for c=7/10, m=4. We provide explicit Hamiltonians on Majorana chains realizing these fermionic minimal models.