In this paper, we introduce valid parametric covariance models for univariate and multivariate spatio-temporal random fields. In contrast to the traditional models, we allow the model parameters to vary over time. Since variables in applications usually exhibit seasonality or changes in dependency structures, the allowance of varying parameters would be beneficial in terms of improving model flexibility. Conditions in constructing valid covariance models and discussions on practical implementation will be provided. As an application, a set of air pollution data observed from a monitoring network will be modeled. It is found that the time varying model performs better in prediction compared with the traditional models.