Single pulse laser excitation at 656 nm and successive pulse excitation at 635.2 and 648.4 nm produced blue emission at 480 nm by two-step upconversion process in Tm³⁺:LaF₃. The excited-state absorption cross-section of the ³F₄ to ¹G₄ transition was estimated by a looping mechanism with cross-relaxation processes. The dynamics of up-conversion andthe possibility of the photon avalanche by a pulse laser excitation were studied by numerical simulation with the rate equation model.