may I can apply f type of visa without invitation letter from china ?

Dear, if you want to apply for an F type, an invitation letter is necessary.
But you said you come to PRC for tourism purpose, you need to apply for a tourist L type. In this case, invitation letter is not necessary. You just need to provide your passport and its copy, the application form affixed with a passport-sized photo, round trip air tickets and hotel reservation. And then submit your application to the embassy of PRC to apply for it.