To assess the effectiveness of the containment strategies proposed in Japan, an SEIAQR (susceptible-exposed-infected-asymptomatic-quarantined-recovered) model was established to simulate the transmission of COVID-19. We divided the spread of COVID-19 in Japan into different stages based on policies. The effective reproduction number Re and the transmission parameters were determined to evaluate the measures conducted by the Japanese Government during these periods. On 7 April 2020, the Japanese authority declared a state of emergency to control the rapid development of the pandemic. Based on the simulation results, the spread of COVID-19 in Japan can be inhibited by containment actions during the state of emergency. The effective reproduction number Re reduced from 1.99 (before the state of emergency) to 0.92 (after the state of emergency). The transmission parameters were fitted and characterized with quantifiable variables including the ratio of untracked cases, the PCR test index and the proportion of COCOA app users (official contact confirming application). The impact of these variables on the control of COVID-19 was investigated in the modelling analysis. On 8 January 2021, the Japanese Government declared another state of emergency. The simulated results demonstrated that the spread could be controlled in May by keeping the same strategies. A higher intensity of PCR testing was suggested, and a larger proportion of COCOA app users should reduce the final number of infections and the time needed to control the spread of COVID-19.