Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the validity of using pure-jump models. However, these tests suffer from several drawbacks, such as requiring rather stringent conditions and having slow rates of convergence. In this paper, we propose a different test to check whether the underlying process of high-frequency data can be modeled by a pure-jump process. The new test is based on the realized characteristic function, and enjoys a much faster convergence rate of order $O(n^{1/2})$ (where $n$ is the sample size) versus the usual $o(n^{1/4})$ available for existing tests; it is applicable much more generally than previous tests; for example, it is robust to jumps of infinite variation and flexible modeling of the diffusion component. Simulation studies justify our findings and the test is also applied to some real high-frequency financial data.