Nonlinear frequency conversion offers an effective way to expand the laser wavelength range based on birefringence phase matching (BPM) or quasi-phase-matching (QPM) techniques in nonlinear crystals. So far, efficient high-harmonic generation is enabled only via multiple cascaded crystals because of the extreme difficulty to simultaneously satisfy BPM or QPM for multiple nonlinear up-conversion processes within a single crystal. Here we report the design and fabrication of a chirped periodic poled lithium niobate (CPPLN) nonlinear crystal that offers controllable multiple QPM bands to support 2nd-8th harmonic generation (HG) simultaneously. Upon illumination of a mid-IR femtosecond pulse laser, we observe the generation of an ultrabroadband visible white light beam corresponding to 5th-8th HG with a record high conversion efficiency of 18%, which is high compared to conventional supercontinuum generation, especially in the HG parts. Our CPPLN scheme opens up a new avenue to explore and engineer novel nonlinear optical interactions in solid state materials for application in ultrafast lasers and broadband laser sources.