This paper provides a new linear time-varying regression with dynamic conditional correlation (DCC) estimated by Gaussian and Student-t copulas for forecasting financial volatility. Time-varying parameters will be estimated for nonparametric dependence by using copula functions with United States stock market data. We compare our model with Kim et al.’s (2016) linear time-varying regression (LTVR) with DCC–GARCH in the ex-post volatility forecast evaluations. Empirical study shows that our proposed volatility models are more efficient than the LTVR model. We also use the superior predictive ability and the reality check for data snooping. Evidence can be found supporting that our proposed model with copula functions provides superior forecasts for volatility over the LTVR model.