  In this work, we investigate the bound states in the continuum (BIC) of a
one-dimensional spin-1 flat band system. It is found that, when the potential
is sufficiently strong, there exists an effective attractive potential well
surrounded by infinitely high self-sustained barriers. Consequently, there
exist some BIC in the effective potential well. These bound states are
protected by the infinitely high potential barriers, which could not decay into
the continuum.} Taking a long-ranged Coulomb potential and a short-ranged
exponential potential as two examples, the bound state energies are obtained.
For a Coulomb potential, there exists a series of critical potential strengths,
near which the bound state energy can go to infinity. For a sufficiently strong
exponential potential, there exists two different bound states with a same
number of wave function nodes. The existence of BIC protected by the
self-sustained potential barriers is quite a universal phenomenon in the flat
band system under a strong potential. A necessary condition for the existence
of BIC is that the maximum value of potential is larger than two times band
gap.

Quantum Gases;Other Condensed Matter