The chaotic dynamics of Lagrangian motion of particles in a steady Arnold–Beltrami–Childress (ABC) flow and a pseudoturbulence are investigated and the Lyapunov exponents and fractal dimensions of particle trajectories for different particle inertia and particle drift velocity are computed. The dispersion process of particles could be characterized by the fractal dimension and dispersion coefficients. The interesting behavior of fractal dimension of particle motion in ABC flow suggested the similarity of particle motion in ABC flow and in a mixing layer. The relationship between particle dispersion coefficient and fractal dimension was nearly linear for the pseudoturbulence.