Generation of attosecond bunches of energetic electrons offers significant potential from ultrafast physics to novel radiation sources. However, it is still a great challenge to stably produce such electron beams with lasers, since the typical subfemtosecond electron bunches from laser-plasma interactions either carry low beam charge, or propagate for only several tens of femtoseconds. Here we propose an all-optical scheme for generating dense attosecond electron bunches via the interaction of an intense Laguerre-Gaussian (LG) laser pulse with a nanofiber. The dense bunch train results from the unique field structure of a circularly polarized LG laser pulse, enabling each bunch to be phase-locked and accelerated forward with low divergence, high beam charge and large beam-angular-momentum. This paves the way for wide applications in various fields, e.g., ultrabrilliant attosecond x/γ-ray emission.