Higher-order interactions between coupled oscillators in neural networks exhibit a series of collective behavior phenomena, especially synchronization, some of which cannot occur in pairwise interactions. Thus far, there has been little researches on whether the higher-order interactions affect other collective behaviors besides synchronization, such as the entrainment ability of the suprachiasmatic nucleus (SCN), which is a master clock located in the mammalian brain. In this article, we investigated whether the entrainment range of the SCN is affected by the second-order interactions, based on a modified Kuramoto model. The numerical simulations and theoretical analyses both showed that the entrainment range is widened by introducing the second-order interactions in the case that a part of the SCN neurons are sensitive to the light information. It was worth noting that the entrainment range depends on the different initial values of the neuronal oscillator phases, and this dependence has not been observed in previous studies of the pairwise interactions. Our findings help to understand the effect of higher-order interactions between the coupled neuron oscillators on the entrainment range of the SCN.