A simple collisional–radiative model for the Paschen 1s and 2p levels is proposed for low-temperature argon discharges. This model can predict the population distribution of 1s and 2p levels over a wide discharge pressure range 1–10⁵ Pa and ionization ratio range 10⁻⁶–10⁻³. The modelling results are found to be in good agreement with observed optical emissions from several different types of argon discharges at 1, 100 and 10⁵ Pa. By using the model, the dominant kinetic processes of 1s and 2p levels are investigated for an electron beam plasma, an inductively coupled plasma, a capacitively coupled plasma and a microwave microplasma. A kinetic diagram is given, which can be used to identify the kinetic state of 1s and 2p levels in many low-temperature argon discharges reported in the literature. This model is also useful for obtaining discharge parameters from optical emissions in low-temperature argon discharges.