The ongoing Zika virus (ZIKV) epidemic poses a major global public health emergency as it has been reported in more than 70 countries worldwide. It is well-known that ZIKV is spread by Aedes mosquitoes, studies show that ZIKV can also be transmitted via sexual contact and cases of sexually transmitted ZIKV of the current outbreak have been confirmed in several countries. In this talk we first present a mathematical model to investigate the impact of mosquito-borne transmission and sexual transmission on prevention and control of ZIKV and use the model to fit the ZIKV data up to February 2016 in Brazil, Colombia, and El Salvador. Our result indicates that sexual transmission increases the risk of infection and epidemic size and prolongs the outbreak. Then we will introduce a second model to describe how Zika virus can be imported, established and spread in new territories by international travel. The model will be used to simulate the non-travel-related infection cases reported in Florida in 2016. In order to prevent and control the transmission of ZIKV, it must be treated as not only a mosquito-borne disease but also a sexually transmitted disease.