The scattering process of an unpolarized Bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x- and y-polarized Bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized Bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the Bessel beam.