Teegarden’s Star b, a nearby terrestrial world receiving an Earth-like instellation, is a prime candidate for next-generation observatories targeting temperate exoplanets in their habitable zones. We employ a suite of three-dimensional global climate model simulations to (1) map the inner boundary of the habitable zone of Teegarden’s Star b and (2) characterize its surface climate under the assumption of an Earth-analog atmosphere. Our simulations show that, with its most recently estimated instellation of 1481 W m⁻², Teegarden’s Star b remains below the runaway greenhouse threshold for both low (α_s = 0.07, ocean-dominated) and moderate (α_s = 0.30, land-dominated) surface albedos. However, a different estimate of 1565 W m⁻² places it beyond the runaway threshold. The result that Teegarden’s Star b is habitable under the most recent instellation measurement reinforces its status as one of the most compelling targets for future habitability and biosignature searches. Given the planet’s proximity to the runaway threshold, it would benefit from a comparative study done with other models using different parameterizations.