Optical bistability and luminescence switching of visible-infrared emission in Tm-doped laser crystal pumped at 648nm avalanche wavelength is predicted theoretically and studied numerically. The analytical formula of luminescence switching threshold is deduced using the theory of nonlinear rate equations. The evolutions of populations of Tm3+ energy levels, emission spectrum and fluorescence intensity versus pump power are investigated numerically. The numerical results predict that the luminescence switching between 452/469nm blue and 1716nm infrared spectra can be experimentally realized under 648nm laser pumping. Moreover, the bistability of emission spectra, chromatic fluorescence and luminescence intensity in Tm-doped crystal can be observed in the vicinity of photon avalanche threshold. The characteristics of chromatic bistability and luminescence switching in Tm-doped crystal allow for the tailoring of pump-controlled all-solid luminescent switcher and bistable wavelength switch operating in visible-infrared spectral range.