Burst-firing in distinct subsets of thalamic relay (TR) neurons is thought to be a key requirement for the propagation of absence seizures. However, in the well-regarded Genetic Absence Epilepsy Rats from Strasbourg (GAERS) model as yet there has been no link described between burst-firing in TR neurons and spike-and-wave discharges (SWDs). GAERS ventrobasal (VB) neurons are a specific subset of TR neurons that do not normally display burst-firing during absence seizures in the GAERS model, and here, we assessed the underlying relationship of VB burst-firing with Ih and T-type calcium currents between GAERS and non-epileptic control (NEC) animals. In response to 200-ms hyperpolarizing current injections, adult epileptic but not pre-epileptic GAERS VB neurons displayed suppressed burst-firing compared to NEC. In response to longer duration 1,000-ms hyperpolarizing current injections, both pre-epileptic and epileptic GAERS VB neurons required significantly more hyperpolarizing current injection to burst-fire than those of NEC animals. The current density of the Hyperpolarization and Cyclic Nucleotide-activated (HCN) current (Ih) was found to be increased in GAERS VB neurons, and the blockade of Ih relieved the suppressed burst-firing in both pre-epileptic P15-P20 and adult animals. In support, levels of HCN-1 and HCN-3 isoform channel proteins were increased in GAERS VB thalamic tissue. T-type calcium channel whole-cell currents were found to be decreased in P7-P9 GAERS VB neurons, and also noted was a decrease in CaV3.1 mRNA and protein levels in adults. Z944, a potent T-type calcium channel blocker with anti-epileptic properties, completely abolished hyperpolarization-induced VB burst-firing in both NEC and GAERS VB neurons.