High-dimensional time series data are frequently encountered in imaging studies and graphical models have been used to assess brain connectivity. In these models, it is common to assume that the variables are multivariate normal yielding the classical Gaussian graphical model. However, violation of the distributional assumption can lead to biased statistical estimates and interpretations. To address this issue, we propose a new semiparametric transformation Gaussian graphical model, in which the time series of each variable of interest are multivariate normal conditional on the covariates after an unspecified transformation. The proposed model also accounts for the correlations amongst time series data through the use of random effects. We propose a three-step procedure to construct the graph. Extensive simulation studies demonstrate that the proposed model outperforms the existing methods when the model assumptions are violated and is comparable to the existing methods under the true model specification. An application to a real data set is also provided.