  We generalize the $(n+1)$-dimensional twisted $R$-Poisson topological sigma
model with flux on a target Poisson manifold to a Lie algebroid. Analyzing
consistency of constraints in the Hamiltonian formalism and the gauge symmetry
in the Lagrangian formalism, geometric conditions of the target space to make
the topological sigma model consistent are identified. The geometric condition
is an universal compatibility condition of a Lie algebroid with the
multi-symplectic structure. This condition is a generalization of the momentum
map theory of a Lie group and is regarded as a generalization of the momentum
section condition of the Lie algebroid.
