As global warming is proceeding due to rising greenhouse gas concentrations, the Earth system moves towards climate states that challenge adaptation. Past Earth system states are offering possible modelling systems for the global warming of the coming decades. These include the climate of the mid-Pliocene (similar to 3 Ma), the last interglacial (similar to 129-116 ka) and the mid-Holocene (similar to 6 ka). The simulations for these past warm periods are the key experiments in the Paleoclimate Model Intercomparison Project (PMIP) phase 4, contributing to phase 6 of the Coupled Model Intercomparison Project (CMIP6). Paleoclimate modelling has long been regarded as a robust out-of-sample test bed of the climate models used to project future climate changes. Here, we document the model setup for PMIP4 experiments with EC-Earth3-LR and present the large-scale features from the simulations for the mid-Holocene, the last interglacial and the mid-Pliocene. Using the pre-industrial climate as a reference state, we show global temperature changes, large-scale Hadley circulation and Walker circulation, polar warming, global monsoons and the climate variability modes - El Nino-Southern Oscillation (ENSO), the Pacific Decadal Oscillation (PDO) and the Atlantic Multidecadal Oscillation (AMO). EC-Earth3-LR simulates reasonable climate responses during past warm periods, as shown in the other PMIP4-CMIP6 model ensemble. The systematic comparison of these climate changes in past three warm periods in an individual model demonstrates the model's ability to capture the climate response under different climate forcings, providing potential implications for confidence in future projections with the EC-Earth model.