Traditional thermal/epithermal neutron multiplicity counting systems based on 3He tubes have relatively low measurement accuracy and high development costs. Fast neutron multiplicity counting (FNMC) technique based on liquid scintillation detectors has become a research hotspot. However, fast neutron multiplicity counting systems currently built are still in the experimental research stage. [Purpose]: This study aims to develop a passive fast neutron multiplicity counting system that can be used for practical measurement. [Method]: Firstly, a passive fast neutron multiplicity counting system was built using 32 self-developed EJ-309 liquid scintillation detectors. To improve the uniformity of neutron detection efficiency of the system, these detectors are arranged in a spherically symmetrical geometry. The system also integrates a self-designed and developed 32-channel high-voltage power supply and a user-friendly graphical interface. Secondly, the Doubles parameter fitting method and the three-parameter fast neutron multiplicity analytical method are used to evaluate the spontaneous fission rates of the 252Cf neutron sources respectively. Finally, the performance of the system under different neutron radiation backgrounds (with Singles rates of 111.42±0.46, 73.97±0.28, and 47.27±0.29, respectively) was also evaluated. [Results]: The experimental results show that the Doubles parameter fitting method can accurately evaluate the spontaneous fission rates of 252Cf neutron sources. The relative differences of the spontaneous fission rates of the 252Cf neutron sources evaluated by using the fast neutron multiplicity analytical method are less than ±4%. The measurement results under different neutron radiation backgrounds are basically consistent with those under natural environment background (the Singles rates were 0.51±0.02). [Conclusion]: The FNMC system can accurately determine the spontaneous fission rate of the 252Cf neutron source (with an equivalent 240Pueff mass range of 5.37-209.62g), and has very good anti-background interference capabilities.