Since the unsteadiness of tip leakage flow has profound effects on both aerodynamic performance and stall margin of axial compressors, it is important to accurately predict the transient tip flow at affordable computational cost. Limited by the high requirement of grid resolution of wall turbulence flow, large eddy simulation (LES) method is greatly restricted in engineering application. In the present work, a Reynolds-stress-constrained large eddy simulation (CLES) method has been introduced, in which the whole domain is simulated using LES while Reynolds stress constraint is enforced on the subgrid-scale (SGS) stress model for near-wall regions aiming at reducing the near-wall grid resolution. The CLES simulations have been performed to investigate the flow behaviors of the unsteady tip leakage flow in a transonic compressor NASA Rotor 67 at near-stall conditions. Reliability assessments have been conducted through comparisons of experimental measurements and numerical results obtained by RANS, DES, CLES as well as LES, respectively. Both the total pressure ratio and isentropic efficiency calculated by CLES agree well with experiment. The turbulence statistical results show three distinct high flow fluctuation regions near the blade tip. The first one is a long and narrow strip ahead of the leading edge of the rotor caused by the movement of the passage shock wave. The second one is formed on the suction side from the leading-edge of the rotor blade due to the oscillation of the tip leakage vortex. And the third one, which occupies most of the blade passage from the middle part of the rotor blade, is generated under multiple factors. The frequency characteristic of the unsteady tip leakage flow has been analyzed. The energy spectrums of the local transient pressure signals are highly related with the local unsteady flow features. The originating mechanisms of the flow unsteadiness in the rotor tip leakage flow have also been discussed, and the results show that the flow unsteadiness is mainly caused by a combined interaction effect of the double leakage flow, the tip leakage vortex flow spilled from the adjacent blade passage, as well as the involved main flow.