Intrinsic optical bistability （IOB） in Tm3+/Yb3+ codoped laser crystal under 650 nm laser excitation is theoretically studied. Based on the theory of nonlinear coupled rate equations, we numerically analyze IOB evolutions of the populations at Tm3+/Yb3+ energy levels, and the influence of system parameters on IOB and the dynamic operation of bistable hysteresis loop. The simulation result shows the fluorescence IOB in visible-infrared spectra of Tm3+/Yb3+ codoped laser crystal under photon avalanche pumping scheme. It is found that IOB phenomena can be largely enhanced by optimizing the Tm3+/Yb3+ concentration ratio, choosing low phonon-energy crystal host and using crystal cooling technology, and also by tuning the pump laser to match the resonant frequency of Tm3+ excited-state absorption transition. Through tuning the pump laser wavelength and adjusting the rate of change in pump intensity, the controllable IOB switching can be achieved.