  In this work, we construct an exact projector Hamiltonian with interactions,
which is given by a sum of mutually commuting operators called stabilizers. The
model is based on the recently studied Creutz-ladder of fermions, in which
flat-band structure and strong localization are realized. These stabilizers are
local integrals of motion from which many-body localization (MBL) is realized.
All energy eigenstates are explicitly obtained even in the presence of local
disorders. All states are MBL states, that is, this system is a full many-body
localized (FMBL) system. We show that this system has a topological order and
stable gapless edge modes exist under the open boundary condition. By the
numerical study, we investigate stability of the FMBL and topological order.
