In classical linear optics, when light shines upon a grating in the normal configuration where the incident plane of light is perpendicular to the optical axis of grating, ordinary Bragg diffraction will occur. But when light is incident in the general conical configuration where the incident plane of light is oblique to the optical axis of grating, the Bragg diffraction becomes much more complicated. What happens to nonlinear diffraction of laser beam by a nonlinear grating? In this paper we wish to answer this interesting and fundamental question in the realm of nonlinear optics. We shine a Ti:Sapphire femtosecond pulse laser beam (with central wavelength at 800 nm) upon a periodically poled lithium niobate (PPLN) thin plate nonlinear grating, and systematically investigate the Raman-Nath nonlinear diffraction (NRND) pattern of second-harmonic generation (SHG) laser beam in various conical configurations characterized by both the polar angle and azimuthal angle . By analyzing the diffraction characteristic and uncovering the underlying mechanisms of conical NRND nonlinear diffraction, we have provided a comprehensive understanding of its spatial behavior. The study of conical nonlinear diffraction would enrich the understanding of complicated interaction between the pump laser beam and the structured nonlinear medium and broaden the arena of nonlinear optics.