Spin squeezing and quantum entanglement have significant and widespread applications in quantum information processing. Therefore, how to generate spin squeezing and quantum entanglement in various quantum systems has become a very important research topic. In this paper, we theoretically investigate how to generate spin squeezing and quantum entanglement in the Lipkin-Meshkov-Glick model. Using spin-wave approximation, we analytically calculate the effects of the spin-spin interaction parameter and the linear interaction parameter on quantum entanglement and spin squeezing. The results show that spin squeezing and quantum entanglement can be periodically generated by adjusting the linear interaction strength, spin-spin interaction strength and its evolution time. And it is also shown that the smaller the linear interaction parameter or the stronger the spin-spin interaction, the better the entanglement and spin squeezing, and the larger the period.