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Abstract Using plasma mirror injection we demonstrate, both analytically and numerically, that a circularly polarized helical laser pulse can accelerate highly collimated dense bunches of electrons to several hundred MeV using currently available laser systems. The circular-polarized helical (Laguerre–Gaussian) beam has a unique field structure where the transverse fields have helix-like wave-fronts which tend to zero on-axis where, at focus, there are large on-axis longitudinal magnetic and electric fields. The acceleration of electrons by this type of laser pulse is analyzed as a function of radial mode number and it is shown that the radial mode number has a profound effect on electron acceleration close to the laser axis. Using three-dimensional particle-in-cell simulations a circular-polarized helical laser beam with power of 0.6 PW is shown to produce several dense attosecond bunches. The bunch nearest the peak of the laser envelope has an energy of 0.47 GeV with spread as narrow as 10%, a charge of 26 pC with duration of ∼ 400 as, and a very low divergence of 20 mrad. The confinement by longitudinal magnetic fields in the near-axis region allows the longitudinal electric fields to accelerate the electrons over a long period after the initial reflection. Both the longitudinal E and B fields are shown to be essential for electron acceleration in this scheme. This opens up new paths toward attosecond electron beams, or attosecond radiation, at many laser facilities around the world.