Dynamics of micrometer-sized dielectric objects can be controlled by optical tweezers with scanning light, however, the trapped objects fail to track the scan when drag exceeds the trapping by too quick movement. On the other hand, optical vortices (OVs), which have a property of carrying angular momenta, can directly control torque on objects rather than their position. Laguerre-Gaussian (LG) beams are the most familiar examples of OV and have been studied extensively so far. Revolution of the objects trapped by the LG beams provides typical models of nonequilibrium statistical system, but stable mid-water trapping by the LG beams becomes essential to evaluate physical properties of the system without extrinsic hydrodynamic effects,. Nevertheless, off-axis revolutions of small objects trapped in mid-water by the LG beams have not yet been established with secure evidences. Here we report stable off-axis trapping of dielectric spheres in mid-water using high-quality LG beams generated by a holographic complex-amplitude modulation method. Direct evidence of the three-dimensional off-axis LG trapping was established via estimating the trapping position by measuring the change of revolution radii upon pressing the spheres onto glass walls. Resultantly, the axial trapping position was determined as about half the wavelength behind the beam waist position. This result provides a direct scientific evidence for possibility of off-axis three-dimensional trapping with a single LG beam, moreover, suggests applications as powerful tools for studying energy-conversion mechanisms and nonequilibrium nature in biological molecules under torque.