In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no nontrivial Dirac particle which is Lp for 0 < p ⩽ $$\frac{4}{3}$$ 4 3 with arbitrary eigenvalue λ, and for $$\frac{4}{3}$$ 4 3 < p ⩽ $$\frac{4}{3-2q}$$ 4 3 − 2 q , 0 < q < $$\frac{3}{2}$$ 3 2 with eigenvalue |λ| > |Q|+qκ, outside and away from the event horizon. By taking q = $$\frac{1}{2}$$ 1 2 , we show that there is no normalizable massive Dirac particle with mass greater than | Q| + $$\frac{\kappa}{2}$$ κ 2 outside and away from the event horizon in non-extreme Kerr-Newman-AdS spacetime, and they must either disappear into the black hole or escape to infinity, and this recovers the same result of Belgiorno and Cacciatori in the case of Q = 0 obtained by using spectral methods. Furthermore, we prove that any Dirac particle with eigenvalue |λ| < $$\frac{\kappa}{2}$$ κ 2 must be L2 outside and away from the event horizon.