This paper proposes a new class of characteristic-function-based distribution tests. The proposed tests are easy to compute and have the asymptotic null distribution chi-square(2). As compared to the Kolmogorov-Smirnov and Cramer-von Mises tests, the proposed test can flexibly account for distribution information at different frequency. A Monte Carlo simulation shows that the proposed test performs quite well. In an empirical study of stock index returns, we apply the proposed test to check distribution assumptions of the GARCH(1,1) model's standardized errors. This test accepts the standardized t distribution but strongly rejects standard normal distribution. Performance of the logistic, generalized error, and generalized lambda distributions are data-specific. This study also shows that the conditional normality assumption may render the GARCH(1,1) model over-estimating the impact effect of external shocks on volatility but under-estimating the persistence of these shocks' influences, especially when the markets are volatile.