In this paper, we investigate an initial-boundary value problem for the self-consistent chemotaxis-Navier-Stokes system { n t + u · ∇ n = ∆ n − ∇ · ( n ( 1 + n ) − α ∇ c ) + ∇ · ( n ∇ ϕ ) , x ∈ Ω , t > 0 , c t + u · ∇ c = ∆ c − c + n , x ∈ Ω , t > 0 , u t + κ ( u · ∇ ) u + ∇ P = ∆ u − n ∇ ϕ + n ( 1 + n ) − α ∇ c , x ∈ Ω , t > 0 , ∇ · u = 0 , x ∈ Ω , t > 0 , where Ω ⊂ R 2 is a bounded domain with smooth boundary, α>0, κ∈R and the gravitational potential function ϕ ∈ W 2 , ∞ ( Ω ) . The novelty of this work lies in the consideration of both the effect of gravity (potential force) on cells and the influence of chemotactic force on the fluid, resulting in a stronger coupling mechanism than that observed in the usual chemotaxis-Navier-Stokes model studied in most existing literatures. It is shown that if α > 1 4 , then for any sufficiently regular initial data, this system admits at least one global and bounded solution to this system under no-flux boundary conditions for n, c and homogeneous Dirichlet boundary condition for u. Our analytic approach is based on a new energy-like functional ∫ Ω n 1 + k 0 α + ∫ Ω | ∇ c | 2 with some integer k 0 > 3 α .