A novel technique to generate precisely size-controlled hollow beams by controlling the diameter of circular slit is proposed. Firstly, a laser beam is transformed into a quasi-monochromatic incoherent annular source by a rotating ground-glass disk and circular slit. Then, after passing through a thin converging lens, a J0-correlated Schell-model beam is synthesized by placing the annular incoherent source in the first focal plane of the thin lens. Finally, a partially coherent hollow beam is generated by focusing the J0-correlated Schell-model beam with an axicon. Based on the diffraction theory and the propagation law of partially coherent beams, the cross-spectral density function is derived to calculate the intensity distribution of the cross section and the radial intensity distribution along the propagation axis behind the axicon. By carrying out the theoretical calculation, the proposed optical system generates a partially hollow beam, and the size of the hollow beam expands continuously as the propagation distance increases. Before further investigating the effect of the diameter of incoherent annular source on the hollow beam behind the axicon, we also calculate the intensity distribution of the cross section and the size of hollow beams along the propagation axis at z=70 mm with the source diameters being 1, 2, 3, 4 and 5 mm, respectively. Results show that the size of the hollow beam also increases with the diameter of incoherent annular source increasing. In this case, the size of the hollow beam can be precisely controlled by tuning the diameter of incoherent annular source through circular slit. We also design and conduct an experimental generation of the hollow beam and investigate the propagation properties. In the experiment, we control the diameter of the annular source by tuning the diameter of the circular slit located before the rotating ground-glass disk. And the diameter of the annular source is equal to that of the circular slits. When the sizes of circular slits are 1, 2, 3, 4 and 5 mm, respectively, the corresponding hollow beams are measured by CCD. Experimental results show that the size of hollow beam can be controlled by the propagation distance and the diameter of the circular slit. The intensity profiles are in good agreement with theoretical predictions. Therefore, the size of hollow beams can be precisely generated and controlled by the proposed system so that the optical system can be flexibly employed in optical trapping and manipulation of particles with different sizes. The results may provide a powerful tool for manipulating the micro- and nano-particles.