Motivated by a recent experiment on the rare-earth material [Y. Li , Phys. Rev. Lett. 115, 167203 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.167203], which found that the ground state of is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin- model that was proposed to describe . Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a phase and two distinct stripe phases. The transitions from the two stripe phases to the phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material . These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in .