The COVID-19 pandemic has affected all domains of human life, including the economic and social fabric of societies. One of the central strategies for managing public health throughout the pandemic has been through persuasive messaging and collective behaviour change. To help scholars better understand the social and moral psychology behind public health behaviour, we present a dataset comprising of 51,404 individuals from 69 countries. This dataset was collected for the International Collaboration on Social & Moral Psychology of COVID-19 project (ICSMP COVID-19). This social science survey invited participants around the world to complete a series of moral and psychological measures and public health attitudes about COVID-19 during an early phase of the COVID-19 pandemic (between April and June 2020). The survey included seven broad categories of questions: COVID-19 beliefs and compliance behaviours; identity and social attitudes; ideology; health and well-being; moral beliefs and motivation; personality traits; and demographic variables. We report both raw and cleaned data, along with all survey materials, data visualisations, and psychometric evaluations of key variables.