We demonstrate, both theoretically and experimentally, a kind of fan-shaped optical beam propagating along the arbitrary trajectories (such as parabolic, hyperbolic and three-dimensional spiraling trajectories). With a controlled profile, this fan-shaped optical beam can be obtained from superposition of the Bessel-like beam and vortex Bessel-like beam. Also, the ability of guiding and transporting microparticles along its lobes is explored. These beams may find a variety of applications in optical trapping and manipulation. [ABSTRACT FROM AUTHOR]