A theoretical study of the kinetics of two-step-excitation upconversion ultraviolet cw fiber laser based on the 4f5d state in Pr^(3+):ZBLAN is performed using steady population rate equations and light propagation equations. Under different Pr^(3+) concentrations, the dependence of the threshold pump powers on the other pump power, the variations of laser output power with reflectivity of output coupler, pump powers and fiber length as well as the dependence of the optimum fiber length on pump powers are investigated. The results predict some optimum laser parameters for maximizing output power.