We investigate the sensitivities on the Wilson coefficients of dimension-six operators associated with the anomalous Hyy, HyZ and HZZ vertices through the process N-N+ -> Zyy at future muon collider. Signal events involving Higgs-gauge boson interactions and relevant backgrounds events at the muon collider designed with a center-of-mass energy of 10 TeV and an integrated luminosity of 10 ab-1 are generated in Madgraph within the framework of the model-independent Standard Model effective field theory. Realistic detector effects of the muon collider detector are simulated by Delphes. The limits at 95% C.L., 3a and 5a on the coefficients cHB and cHW are obtained without and with systematic uncertainty of 15% and compared with the present experimental and phenomenological limits.