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We show that a ring-shaped hollow electron beam can be injected and accelerated by using a Laguerre-Gaussian laser pulse and ionization-induced injection in a laser wakefield accelerator. The acceleration and evolution of such a hollow, relativistic electron beam are investigated through three-dimensional particle-in-cell simulations. We find that both the ring size and the beam thickness oscillate during the acceleration. The beam azimuthal shape is angularly dependent and evolves during the acceleration. The beam ellipticity changes resulting from the electron angular momenta obtained from the drive laser pulse and the focusing forces from the wakefield. The dependence of beam ring radius on the laser-plasma parameters (e.g., laser intensity, focal size, and plasma density) is studied. Such a hollow electron beam may have potential applications for accelerating and collimating positively charged particles. [ABSTRACT FROM AUTHOR]