In this work, a new type of energy-absorbing thin-walled tubes with concave angles is proposed by a unique structural design method to improve the crashworthiness performance of the traditional hexagonal thin-walled tube (TH). These concave tube structures (CTSs) are named CTS1, CTS2, and CTS3 respectively, while CTS1 is developed by a common design method. The crushing behaviors of the CTS3 are investigated by quasi-static compression experiments and numerical simulations. The crashworthiness and energy dissipation mechanism of all the tubes are investigated, and the results demonstrate that the CTS3 exhibits superior energy absorption capability than the other proposed tubes and TH with the same mass. Then, the mean crush resistance of the CTSs is predicted by theoretical analysis, and the influences of slenderness rate, boundary condition, and loading rate on the crushing responses of CTS3 are performed by numerical analysis. Besides, the comparative analysis of performances of the CTS3 and the typical concave tubes (TCTs) is carried out, and the results indicate that the CTS3 has the best energy absorption capacity among these tubes. In addition, the optimal structure parameters of CTS3 are explored to enhance the capacity of energy absorption further.