The circuit parameters of spark pin ultroviolet (UV) pre-ionization discharge non-chain pulsed DF laser is researched to improve its discharge uniformity and electric energy depositions. Through analysis the process of dissociation of SF6 molecules and the attachment of electrons to SF6 molecules, the continuity-equations for electrons is obtained. Combination with the Kirchhoff equations for discharge circuit, the mathematical model is established to describe the discharge parameters of DF laser. Based on this model, the voltage waveforms of pre-ionization and main discharge, also the current waveform of main discharge are solved numerically. The results display some physical processes correctly, such as the delay time between pre-ionization and main discharge, breakdown of the main electrode and the self-maintained discharge. Then the corresponding experiments are carried out to verify the results of this model. The measured pre-ionization and main discharge voltage waveforms are consistent with the simulation results. Using this model, the influences of main store capacitance, delay inductance, peak capacitance on the discharge are researched individually, and the circuit parameters of DF laser are obtained that is useful to improve the discharge stability.