Gradient refractive index (GRIN) lens-based chirp signal chirpiness detection usually relies on the fractional Fourier transform (FRFT) functionality of a quadratic GRIN lens and is limited by paraxial conditions. In this paper, a non-FRFT mechanism-based chirpiness detection GRIN lens is proposed that converts the Luneburg lens' focus capacity of input plane waves to the designed lens' focusing of input chirp waves using transformation optics, and the source chirpiness can be obtained by sweeping the illumination wavelength rather than locating the focusing pulse, consequently greatly increasing the upper limit of the chirpiness detection range. The feasibility and robustness of the method are verified through numerical simulations.