Crowdsourcing delivery is becoming a prevalent tool for tackling delivery problems by building a large labor-intensive service network. In this network, the delivery personnel consist of a large number of people with a complex composition and high level of mobility, creating enormous challenges for the quality of service and the management of a crowdsourcing platform. Hence, we attempt to conduct a competence analysis to determine whether they can provide promised services with high quality, i.e., they are competent for their job. To this end, the competence theory is introduced, and a multicriteria competence analysis (MCCA) approach is developed. To illustrate the MCCA approach, a real-world case study is conducted involving a Chinese takeaway delivery platform, where the Bayesian best-worst method is used to determine the weights of the criteria based on the data collected from managers of the platform company. Also, the competence scores of the personnel involved are collected through surveys and data sources of the company. Given the weights and the competence scores, we use additive value function to identify the overall competence scores of them, which reflects the level of competence for their job. The results show that Skills is the most important competence, while Knowledge is the least important of the four competence dimensions. In subcriteria, four core elements are identified such as punctuality, customer service awareness, responsible, and goods intact. In addition to the importance of criteria, a ranking of a sample of personnel is provided, and almost half of the crowdsourcing delivery personnel's competence is below the average and vary significantly, while the relationship between the competence level and some other variables is also discussed. Moreover, the developed MCCA approach in this paper can be applied to analyze the competence of personnel in many other industries as well.