Supercontinuum white laser with large bandwidth and high pulse energy would offer incredible versatility and opportunities for basic science and high technology applications. Here, we report the generation of high-efficiency 2.8-octave-spanning ultraviolet-visible-infrared (UV-Vis-IR) (with 350-2500 nm 25 dB bandwidth) supercontinuum white laser from a single chirped periodically poled lithium niobate (CPPLN) nonlinear crystal via synergic high-harmonic generation (HHG) and self-phase modulation (SPM). The CPPLN exhibits multiple controllable reciprocal-lattice bands to simultaneously support the quasi-phase matching (QPM) for simultaneous broadband 2nd-10th HHG via cascaded three-wave mixing against a broadband fundamental pump laser. Due to the efficient second-order nonlinearity (2nd-NL) up-conversion and significant 3rd-NL SPM effect both in the pump and HHG laser pulses, 350-2500 nm supercontinuum white laser is eventually obtained with 17 μJ per pulse under pump of 45 μJ per pulse mid-infrared femtosecond laser corresponding to an average high conversion efficiency of 37%. Our work opens up a route towards creating UV-Vis-IR all-spectrum white lasers through engineering the synergic action of HHG and SPM effects in nonlinear crystals for applications in ultrafast spectroscopy, single-shot remote sensing, biological imaging, and so on.