On March 11, 2020, the World Health Organization declared COVID-19 a pandemic. The outbreak containment strategies in China based on non-pharmaceutical interventions (NPIs) appear to be effective, but quantitative research is still needed to assess the efficacy of NPIs and their timings. Using epidemiological and anonymised human movement data, here we develop a modelling framework that uses daily travel networks to simulate different outbreak and intervention scenarios across China. We estimated that there were a total of 114,325 COVID-19 cases (interquartile range 76,776 - 164,576) in mainland China as of February 29, 2020. Without NPIs, the COVID-19 cases would likely have shown a 67-fold increase (interquartile range 44 - 94) by February 29, 2020, with the effectiveness of different interventions varying. The early detection and isolation of cases was estimated to have prevented more infections than travel restrictions and contact reductions, but combined NPIs achieved the strongest and most rapid effect. The lifting of travel restrictions since February 17, 2020 does not appear to lead to an increase in cases across China if the social distancing interventions can be maintained, even at a limited level of 25% reduction on average through late April. Our findings contribute to an improved understanding of NPIs on COVID-19 and to inform response efforts across the World.