We report an experimental realization of an adaptive quantum state tomography protocol. Our method takes advantage of a Bayesian approach to statistical inference and is naturally tailored for adaptive strategies. For pure states we observe close to 1/N scaling of infidelity with overall number of registered events, while best non-adaptive protocols allow for 1/\sqrt{N} scaling only. Experiments are performed for polarization qubits, but the approach is readily adapted to any dimension.