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In this paper, the complex network of the urban functions in Shenzhen of China under the lockdown of the corona virus disease 2019 (COVID-19) is studied. The location quotient is used to obtain the dominant urban functions of the districts in Shenzhen before and under the lockdown of COVID-19. By using the conditional probability, the interdependencies between the urban functions are proposed to obtain the complex networks of urban functions and their clusters. The relationships between the urban functions, and the overall and cluster characteristics of the urban functions before and under the lockdown of COVID-19 are analyzed based on the complex networks. The mean degree and mean weighted degree of the primary categories of the urban functions are obtained to discuss the classification characteristics of the urban functions before and under the lockdown of COVID-19. Then, the differences and changes of the urban functions before and under the lockdown of COVID-19 are compared, and the corresponding policy implications under the lockdown of COVID-19 are presented. The results show that under the lockdown of COVID-19, the correlation of the urban functions is stronger than that before the lockdown; the common urban functions are more useful and essential, and finance, fine food and medical treatment are important; public service and government departments have the most positive relationship with other urban functions, and finance service has the highest spatial agglomeration distribution trend; and the cluster characteristics of urban functions are more related to people's livelihood, and the urban functions show incomplete and cannot be operated for long term. [ABSTRACT FROM AUTHOR]