I am a Singaporean who has a F visa but I want to visit Hong Kong, how to get a multiple trips visa?

You can apply for a China visa in HK through the Commissioner's office of the Ministry of China Foreign Affairs. However, if you have not the HK resident status, you can not apply for multi-entry-visa at that office. Your previous China visa is needed as well. If possible, you can apply in Singapore for the multiple entry visa to China.