This paper aims at evaluating the effectiveness of different intervention measures against the infection of avian influenza A (H7N9) by using an epidemiological model. The model formulates the intrinsic interactions of domestic poultry (DP), H7N9 virus and humans by ordinary differential equations and couples the essential roles of various interventions (including culling, vaccinating, screening, disinfecting, and reducing contact rate, etc). Qualitative analysis indicates that when the recruiting poultry is virus-free, there is a transmission threshold denoted by basic reproduction number which can determine the invasion of H7N9; and there is always a stable H7N9 endemic in case of persistent import of virus-carrying poultry, under which only complete vaccination or cutting off poultry-to-poultry/human contacts can stop H7N9 transmission. By performing numerical analysis of the model with biological background parameters, the intervention outcomes against H7N9 infection are further quantified. It is found that (1) reducing poultry-human/poultry interaction and per-contact infection probability, as well as culling DP, are highly effective in diminishing the infections of humans and DP; (2) the disease is prevented when larger than (1 - 0.1λ p ) proportion of DP is vaccinated, where λ p is the DP-to-DP transmission rate; (3) cleaning and disinfecting environment play limited role in reducing the risk of infection; and (4) screening imported poultry is quite important for stopping disease diffusion, but it works little when local epidemic is prevailing. Combing these measures with real situations would be necessary for controlling H7N9 epidemics and reaching one health purpose.