We study the energy spectrum and electronic properties of atwo-dimensional (2D)spinless electron gas in a periodic magnetic field which has the symmetry of a triangular lattice. We show that the energy bands depend strongly on the value of the magnetic field. For large field the low-energy electrons are localized on closed rings where the magnetic field vanishes. This results in the appearance o fpersistent currents around these rings. We also calculate the intrinsic Hall conductivity, which is quantized when the Fermi level is in a gap.