Free electron radiation, particularly Smith-Purcell radiation, provides a versatile platform for exploring light-matter interactions and generating light sources. A fundamental characteristic of Smith-Purcell radiation is the monotonic decrease in radiation frequency as the observation angle increases relative to the direction of the free electrons’ motion, akin to the Doppler effect. Here, we demonstrate that this fundamental characteristic can be altered in Smith-Purcell radiation generated by photonic crystals with left-handed properties. Specifically, we have achieved, to our knowledge, a novel phenomenon that the lower-frequency components propagate forward, while the higher-frequency components propagate backward, which we define as reverse Smith-Purcell radiation. Additionally, this reverse Smith-Purcell radiation can confine the radiation to a narrow angular range, which provides a way to obtain broadband light sources in a specific observation angle. Furthermore, by precisely adjusting the grating geometry and the kinetic energy of the free electrons, we can control both the radiation direction and the output frequencies. Our results provide a promising platform to study unexplored light-matter interactions and open avenues to obtain tunable, broadband light sources.