In the framework of the generalized Lorenz-Mie theory (GLMT), the scattering of arbitrarily incident shaped beam by dielectric bi-sphere is investigated. By expressing the incident beam with arbitrary incidence angle in terms of the spherical vector wave function, we derive the scattering equations of bi-sphere arbitrarily illuminated by a single beam, and then extend to the case of scattering of dual-beam. As an example, numerical computations for the scattered intensities of bi-sphere randomly irradiated by a single Gaussian beam and by two Gaussian beams are presented respectively after numerical verifications. In particular, the scattering properties for the two cases are compared and discussed theoretically in detail with respect to different parameters such as incident angle, center-center separation, etc.