The response of glaciers to climate change has major implications for sea-level change and water resources around the globe. Large-scale glacier evolution models are used to project glacier runoff and mass loss, but are constrained by limited observations, which result in models being over-parameterized. Recent systematic geodetic mass-balance observations provide an opportunity to improve the calibration of glacier evolution models. In this study, we develop a calibration scheme for a glacier evolution model using a Bayesian inverse model and geodetic mass-balance observations, which enable us to quantify model parameter uncertainty. The Bayesian model is applied to each glacier in High Mountain Asia using Markov chain Monte Carlo methods. After 10,000 steps, the chains generate a sufficient number of independent samples to estimate the properties of the model parameters from the joint posterior distribution. Their spatial distribution shows a clear orographic effect indicating the resolution of climate data is too coarse to resolve temperature and precipitation at high altitudes. Given the glacier evolution model is over-parameterized, particular attention is given to identifiability and the need for future work to integrate additional observations in order to better constrain the plausible sets of model parameters.