This paper addresses the problem of angle-of-arrival (AoA) estimation with leaky-wave antennas (LWA), specifically, the necessity to operate over large bandwidth to cover a large field of view. By designing the LWA so that multiple space harmonics contribute to the radiation, a multi-beam operation is achieved that allows covering a large angular range using a limited fractional bandwidth. The MUSIC algorithm is then used in order to estimate AoA without ambiguity among the multiple beams. As an example, simulation results show it is possible to estimate AoA over a 180° angular range with a 1.92% bandwidth.