Motivated by a recent inelastic neutron scattering experiment on $mathrm{YbMgGaO}_4$ cite{William2019}, we reinvestigate the homogeneous spin model on the triangular lattice. Using the cluster mean-field theory, we study the phase diagram and the magnetic-field-induced phase transition. We find that the phase boundary between the stripe state and the $120^{circ}$ antiferromagnetic state is broadened by the magnetic field, leading to a field-induced phase transition. This phase transition is suppressed by the next-nearest neighbor exchange interaction $J_2/J_1$ and vanishes as $J_2/J_1>0.13$. We find a parameter space at $J_2/J_1=0.1$, in which the field-induce transition can be achieved and the deviation of theoretical spin excitation energies from experimental data is only $5.4%$. Our results imply that an effective homogeneous spin model still works in $mathrm{YbMgGaO}_4$.
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