We studied the superfluid Mott-insulator phase transition in an open coupled cavity optomagnonic array system. Based on the quasibosonic approach and employing perturbation approximation and mean-field theory, we obtain the time-dependent analytical superfluid order parameter. We find that dissipation will make the system decoherent and the large magnon-cavity coupling strength will
help the system obtain great coherence. Finally, we the reasons that increasing the magnon-cavity coupling strength leads the system tend to the superfluid phase
through are analyzed. The work holds significant guidance for the study of superfluidMott insulator phase transition under dissipative conditions, and providing a reliable
reference for experimental implementation in open quantum systems.