We propose a novel beam model for radio pulsars based on the scenario that the broadband and coherent emission from secondary relativistic particles, as they move along a flux tube in a dipolar magnetic field, form a radially extended sub-beam with unique properties. The whole radio beam may consist of several sub-beams, forming a fan-shaped pattern. When only one or a few flux tubes are active, the fan beam becomes very patchy. This model differs essentially from the conal beam models with respect to the beam structure and predictions on the relationship between pulse width and impact angle β (the angle between the line of sight and the magnetic pole) and the relationship between emission intensity and beam angular radius. The evidence for this model comes from the observed patchy beams of precessional binary pulsars and three statistical relationships found for a sample of 64 pulsars, of which β were mostly constrained by fitting polarization position angle data with the rotation vector model. With appropriate assumptions, the fan beam model can reproduce the relationship between 10% peak pulse width and |β|, the anticorrelation between the emission intensity and |β|, and the upper boundary line in the scatter plot of |β| versus pulsar distance. An extremely patchy beam model with the assumption of narrowband emission from one or a few flux tubes is studied and found unlikely to be a general model. The implications of the fan beam model for the studies on radio and gamma-ray pulsar populations and radio polarization are discussed.
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