In recent years，systemic risk by banks has become an important issue in finance research area．In this paper，we build a novel research framework to measure the inter-bank default contagion and systemic risk by banks．Under the framework，the problem of default algorithm in the present researches is pointed out and rectified．Moreover，the way of establishing scale-free network is put forward to simulate the inter-bank network．It is found that: more banks are infected in a higher-centralized network; the total assets of failed banks are less in higher-centralized networks when there are less banks suffering fundamental defaults．Furthermore， the influence of default contagion caused by large-bank failures in highly-centralized networks is bigger than that in low-centralized networks．Although small-bank failures do not easily bring about contagion，reaching a certain scale，they will also lead to large-bank failures contagiously．