A systematic study of non-inductive current drive via helicity injection by global Alfvén eigenmode (GAE) waves is carried out. For illustration, the first radial mode of the discrete resonant GAE spectrum is considered. The following aspects are given special attention: spectral analysis, radial dependence and efficiency – all of these as functions of the characteristics of the waves launched by an external, concentric antenna (i.e. wave frequency and poloidal and toroidal wavenumbers). The tokamak plasma is simulated by a current-carrying cylindrical plasma column surrounded by a helical sheet current and situated inside a perfectly conducting shell, with incorporation of equilibrium (simulated) toroidal field, magnetic shear and a relatively large poloidal magnetic field component. Within the framework of low-β MHD model equations and for typical tokamak physical parameters, the following basic results are obtained: (1) in the range of poloidal wavenumbers −3[les ]m[les ]3 and toroidal wavenumbers −20[les ]n[les ]20, resonant GAE peaks below the Alfvén continuum are found; (2) the power absorption (P), current drive (I) and corresponding frequency of the GAE modes depend strongly on the sets of (m, n) values considered; (3) the ‘net’ current drive is positive (i.e. flows in the direction of the equilibrium current j0z) for m=−1, −2, −3 and −20[les ]n[les ]−1 as well as for m=+1, +2, +3 and n>10; (4) in the cases m=−1, −2, −3, the efficiency of current drive, I/P, increases with [mid ]m[mid ] and 1/[mid ]n[mid ]; (5) the radial localization of the current drive in each of the cases considered is determined and tabulated.