We study a nonequilibrium model with up-down symmetry and a noise parameter $q$ known as majority-vote model of M.J. Oliveira $1992$ on opinion-dependent network or Stauffer-Hohnisch-Pittnauer networks. By Monte Carlo simulations and finite-size scaling relations the critical exponents $β/ν$, $γ/ν$, and $1/ν$ and points $q_{c}$ and $U^*$ are obtained. After extensive simulations, we obtain $β/ν=0.230(3)$, $γ/ν=0.535(2)$, and $1/ν=0.475(8)$. The calculated values of the critical noise parameter and Binder cumulant are $q_{c}=0.166(3)$ and $U^*=0.288(3)$. Within the error bars, the exponents obey the relation $2β/ν+γ/ν=1$ and the results presented here demonstrate that the majority-vote model belongs to a different universality class than the equilibrium Ising model on Stauffer-Hohnisch-Pittnauer networks, but to the same class as majority-vote models on some other networks.