The recently proposed compressed sensing (CS) method sheds light on quantum state tomography of multi-qubit systems with low rank,which greatly reduces the complexity of measurement and computation.However,the restricted isometry property requirement of CS is difficult to be promised or verified in practice,which makes this method probably assign unreasonable results.In regard to this problem,we adopt a two-step procedure and implement an adaptive strategy to update measurement operators based on the measurement results of the first step for CS,which not only serves as a way to verify the estimate but also improves the accuracy of tomography.Our numerical simulations manifest that our adaptive protocol can reduce about half of the infidelity of nonadaptive protocol and is still efficient even when the rank of the state is slightly high,which would greatly benefit multi-qubit state tomography in future experiments.