Can I apply for a passport with a criminal record?

Of course. You can apply for a passport with a criminal record, but you can't apply for a passport according to the law:

According to Article 13 of the Passport Law of the People's Republic of China: "The passport issuing organ shall not issue a passport if the applicant is under any of the following circumstances:

(a) does not have the nationality of People's Republic of China (PRC);

(two) unable to prove identity;

(3) practicing fraud in the application process;

(4) Being sentenced to a penalty and serving a sentence;

(five) the people's court informed that there are unresolved civil cases that cannot leave the country;

(6) Being a defendant or criminal suspect in a criminal case;

(seven) the relevant competent departments of the State Council believe that leaving the country will cause harm to national security or cause great losses to national interests.

Passports of the People's Republic of China are divided into diplomatic passports, official passports and ordinary passports. Ordinary passport holders should have Chinese mainland household registration or be China citizens living abroad.

People's Republic of China (PRC) citizens who are permanent residents of Hong Kong and Macao shall not apply for passports of the People's Republic of China, but shall apply for passports of the People's Republic of China, Hong Kong Special Administrative Region or Macao Special Administrative Region. Residents of Taiwan Province Province who meet certain conditions may apply for passports of the People's Republic of China to relevant institutions in People's Republic of China (PRC) and embassies and consulates abroad.

Baidu Encyclopedia-Passport Law of People's Republic of China