In order to generate a submicron localized hollow laser beam and realize the more efficient laser cooling and trapping of a single atom, a simple and promising scheme with using the system of a single mode fiber a circle binary phase plate and a microlens is proposed in this paper. From Rayleigh-Sommerfeld diffraction theory, the intensity distribution of the generated localized hollow laser beam near the focal plane and its propagating properties in free space are calculated. Also, the dependences of the dark-spot size of the localized hollow beam on the mode radius of single mode fiber and the focal length of the mocrolens are studied. The calculated results show that the intensity distribution of the localized hollow beam presents approximately symmstrical distribution near the focal plane. In the center of the focal plane, the light intensity is 0 and increases gradually around it. So a closed spherical light field (i.e., localized hollow laser beam) with a radius of 0.4 m is generated. The calculated results also show that the dark-spot size of the localized hollow laser beam decreases with the increasing of the microlens focal length and the decreasing of the single mode fiber mode radius. So proper parameters of this optical system can be chosen to generate localized hollow laser beams with different sizes for various applications. When the localized hollow laser beam is blue detuned, atoms will be trapped in the minimum light filed. If a repumping laser beam is applied, the trapped atoms will be also cooled by the intensity-gradient Sisyphus cooling. In this paper, we build a device for trapping and cooling a single atom by using the generated blue detuned submicron localized hollow laser beam. We study the dynamical process of intensity-gradient cooling of a single 87Rb atom trapped in the localized hollow beam by Monte-Carlo method. Our study shows that a single 87Rb atom with a temperature of 120 K (the corresponding momentum is 30ħk) from a magneto-optical trap (MOT) can be directly cooled to a final tempreture of ～ 5.8 K (the corresponding momentum is ～ 6.6ħk). So an ultracold single atom is generated and trapped in our submicro localized hollow beam. This device for obtaining ultralcold single atom can be widely uesd in the regions of the optical physics, the atom and molecule optics, such as the detecting of the fundamental physical parameters, realizing the quantum computer, studying the cold collision of singe atoms, and realizing the single atom laser.